Nary an X or/nor a Y
Solution 1:
Merriam-Webster's Eleventh Collegiate Dictionary (2003), a resource that tends to be parsimonious with its usage labels, identifies nary as a dialect word:
nary adj {alter. of ne'er a} (1848) dial : not any: not one {I must have it back as I have nary other copy —Flannery O'Connor} — nary a or nary an : not a single {survived the accident with nary a scratch}
Dialect words tend to appear in settings where the speaker or writer is less concerned with grammatical nicety than with matching perceived common usage—and in the case of "nary a X nor/or a Y," results on the ground seem to vary.
Thus, for example, "Sporting Adventures of Charles Carrington, Esq." in London Society: An Illustrated Magazine of Light and Amusing Literature (January 1875) has this instance:
'So yeu've come here [to a small town outside New York City] to see our glorious American constitootion. Wall, I guess yeu'll be pretty considerable surprised—tarnation surprised, doggoned if you won't. We're an almighty nation, we air. Going a-shooting, air yeu? Wall, I calkerlate we've got more game hereabouts than would fill all London, and enough ships in our little river the Mississi-pi to tow your little island across the broad Atlantic—we hev, indeed, stranger. There's lots of grouse; but nary a buffeler, bar, nor alligater about here. But I s'pose yeu means to take up yer fixins here in this feather-bed bully hotel afore yeu makes tracks?'
And from Ray Johnstone, Maude Blackstone: The Millionaire's Daughter (1901):
I says tu brother Joshua when we left the ranch to go tu bed, 'Let ius get up before daylight an' harness up our nags, Betsy and Nancy, an' go an' see the elephant'; an' now we've been out on the prairie fer four hours, an' nary an Injun nor nary an' elephant nor tiger have we sot eyes on' ceptin' yerselves, meanin' no offense.
But contrarily, "One of the Towns" in The Western Literary Messenger (Buffalo, New York: February 1857) has this:
Men and women marry, and have children born unto them, and die in the town of German. But there is nary a priest or minister of the gospel, of any denomination, within her borders, to bless the banns, or christen the child, or o give ghostly comfort in the parting hour.
And perhaps most beguilingly, from M.G. McClelland, "Mac's Old Horse," in The Century (July 1888):
Mac cussed hard as he peered around him, / Nary a thing could he find or see; / Never a ghost, nor a witch, nor spirit, / Nor even the trunk of a blasted tree.
This last instance is striking because the writer juxtaposes an instance of "nary a ... or ... with an instance of "Never a ... nor ... nor ... nor ..." Notice, though, that the "or" is used to conjoin two verbs (find and see), whereas the "Nary a" refers to a noun (thing). In contrast, the "Never a ... nor ..." series applies to a set of nouns (ghost, witch, spirit, and trunk) comprehended by the the "Never a" opener. So the usage here may not be inconsistent as a matter of grammatical usage.
Searches for fairly recent instances of the simple case of "Nary a[n] X or/nor Y" yield plenty of matches for both "or" and "nor" forms. The following examples are by no means exhaustive, and most come from a fairly narrow range of publication dates (2002–2008).
Recent examples of 'nary a[n] X nor [a] Y'
From Jerome Lofgren, "Nary a Nose nor Tail," A Town Called Isle (2002):
And the old man would say, "Ne, nary a nose nor tail were seen."
...
"Ne," Grandpa replied sadly. "Nary a nose nor tail were seen." He gave his grandson a wink.
From Joseph Citro, Green Mountain Ghosts, Ghouls & Unsolved Mysteries (1994):
At last the fatal day—March 25, 1844—came and went with nary a bang nor a whimper.
From Robert Sprecht, Tisha: The Story of a Young Teacher in the Alaska Wilderness (1982):
"No race, no stop," he repeated. "C'mon, boy, it's an easy mile, nary a bump nor a bang. How about it?"
From Mae Henderson, Borders, Boundaries, and Frames: Essays in Cultural Studies (1995):
At least, it was something of a shock for me to glance over this year's program for the English Institute and realize that in all the twelve titles for the current talks there was nary a parenthesis, nor a pun, nor a hyphenated term, nor any inverted or disinverted commas: no, there was no point of punctuation more complicated than a colon.
From Dean Budnick, "Jam Bands": North America's Hottest Live Groups (1998):
The Emma Gibbs Band features nary an Emma nor a Gibbs, but the Winston-Salem, North Carolina, sextet does provide some upbeat, jaunty grooves.
From Carolyn Dunn, The Winter Garden Mystery (2001):
Nary a cabbage nor a Brussels sprout dares show its head in the front gardens.
From a 2000 translation by David Assaf of Journey to a Nineteenth-century Shtetl: The Memoirs of Yekhezkel Kotik (2002):
Of all those coming to her father-in-law's house there was nary a rabbi nor a scholar, nor a pious one among them.
From David Barker, Rushed to Judgment: Talk Radio, Persuasion, and American Political Behavior (2002):
In today's political climate, nary a political nor a policy-related decision is made without great consideration being given to how that decision will play out with the electorate[.]
From an unidentified article in Chicago, volume 54 (2005):
It is a sad commentary on an institution we have loved for so long which has let us down time and again with nary an apology nor the accountability of bishops who stand as guilty as perpetrators.
From Thomas Fahey, Considering Aaron Sorkin: Essays on the Politics, Poetics and Sleight of Hand in the Films and Television Series (2005):
To add to the film's emphasis on intelligence rather than beauty or physical attraction, there is nary a love scene nor a scantily clad body in the entire movie.
From Steve Hockensmith, Holmes on the Range (2007):
But there was nary an oyster nor a drop of Scotch, of course.
From Jim Bernhard, Porcupine, Picayune, & Post: How Newspapers Get Their Names (2007):
It is not a comprehensive list of every English-language general-interest newspaper in the world, nor is it a scholarly study with footnoted documentation—nary an ibid. nor an op. cit. will be found in these pages.
From Curtis Badger, A Natural History of Quiet Waters: Swamps and Wetlands of the Mid-Atlantic Coast (2007):
There was nary a blade of grass nor a sprig of sedge to be found.
From Christopher Wren, Walking to Vermont: From Times Square into the Green (2007):
Further ahead, a maroon sign gilded with gold paint announced a new development for Salmon Daily Brook Farm, though nary a brook nor farm nor salmon were in sight.
From Taylor Clark, Starbucked: A Double Tall Tale of Caffeine, Commerce, and Culture (2007):
Nary a chair nor a stool was in sight.
Recent examples of 'nary a[n] X or [a] Y'
From Dana Fewell, Reading Between Texts: Intertextuality and the Hebrew Bible (1992):
It is all good, very good (Gen 1:31), not marred by evil or by any negative; there is nary a no, a not or a nor in Genesis 1.
From Richard Mohr & George Ohr, Pottery, Politics, Art: George Ohr and the Brothers Kirkpatrick (2003):
Nary an eagle, elk, salmon, or Douglas fir is to be found in the inventory of the Kirkpatricks' Nature.
From Mereille Guiliano, French Women Don't Get Fat (2004):
Supermarket cookies and pints of ice cream were always on hand, but nary a fresh vegetable or fruit.
From Steven Raichlen, Raichlen's Indoor! Grilling (2004):
The Rendezvous grills its ribs over an open charcoal fire, with nary a log or hickory chip in sight.
From Michael Nystrom-Schut, Keeping It Real in an Unreal World: Staying as Real as Possible in a World of Illusion (2004):
What's sometimes amazing is how we quietly succumb to the leadership, incredibly so, with nary a whimper or a cry of "foul."
From Elbert Maloney, Chapman Boater's Handbook (2005):
Not only do they stay soft and cozy the whole week long , with nary a rip or tear, they also store in about a quarter of the space taken up by ordinary bed linen.
From Vern Madison & Connie Madison, Living the Dream: Sailing the South Pacific and Southeast Asia (2005):
Our wind vane piloted us flawlessly, with nary a vibration or rattle in the struts, which I had overhauled in Noumea.
From Charles Swartz, Understanding Digital Cinema: A Professional Handbook (2005):
It is interesting to note that many directors pose for photographs, pictured in front of editing devices or sound mixing consoles, albeit with nary an editor or mixer, their necessary collaborators and oftentimes saviors, in frame.
From Fran Sorin, Digging Deep: Unearthing Your Creative Roots Through Gardening (2007):
Never had I envisioned that the ground would be completely bare—with nary a flower or tree in sight!
From Jessica Auerbach, And Nanny Makes Three: Mothers and Nannies Tell the Truth About Work, Love, Money, and each Other (2007):
... Elle Macpherson, "the Body," producing two beautiful sons with nary a stretch mark or increase in the size of her minuscule, butt-hugging, belly—baring jeans; ...
From Tristan Egolf, Kornwolf: A Novel (2007):
But nary a phone call or visit.
From Larry Carlson, Before the Colors Fade: God, Cebu and War (2008):
He swallowed the Garmale with nary a shudder or grimace.
Matt Telles, Python Power!: The Comprehensive Guide (2008):
The early Internet Web pages were plain text, with nary an image or graphic to be seen.
And from David Gilbert, The Normals: A Novel (2008):
Nary a sprain or dislocation, a tear or rupture.
Conclusions
The fact that few of the preceding examples are self-consciously dialectal indicates to me that the word nary is becoming a part of accepted nondialect English, at least in the United States. But because the "nary a[n] X or/nor a Y" formulation arose out of dialect use, it doesn't seem to have benefited (or suffered) from formal enforcement by publishers of a standardized treatment on the question of "or" versus "nor."
One interesting distinction that may not be immediately obvious in the examples I've listed above involves the presence or absence of an indefinite article before the Y term in the phrase. Of the fifteen recent examples of "nary a[n] X nor" listed, twelve conclude with "nor a[n] Y," one with "nor the Y," and two with "nor Y." In sharp contrast, of the fourteen recent examples of "nary a[n] X or" listed, two conclude with twelve "or a[n] Y" and twelve with "or Y." This difference doesn't strike me as being the result of random variation or chance. To the contrary, I think, that most English speakers and writers probably naturally gravitate toward "or" when they are dealing with a "nary a[n] X or/nor Y" situation and toward "nor" when they are dealing with a "nary a[n] X or/nor a[n] Y."
Applying this insight to the poster's original question, I would recommend using either the the wording
Nary a soul or star-nosed mole had I seen for three days ...
or the wording
Nary a soul nor a star-nosed mole had I seen for three days
to the situation he originally proposed. Since souls and star-nosed moles do not make a comfortable natural pairing of similar things I would prefer the second option. But if the situation involved "a white-eyed vireo" instead of "a soul" as the paired object, I don't think you could go wrong with either
Nary a white-eyed vireo or star-nosed mole had I seen for three days ...
or
Nary a white-eyed vireo nor a star-nosed mole had I seen for three days ...