Non-medical or slang synonyms for female reproductive organs

Solution 1:

You might try an authentically medieval English word or two. Chaucer’s Wife of Bath boasts of her own at line 608 of her Prologue:

I hadde the beste quoniam myghte be.

Elsewhere (e.g., Merchant's Tale, line 2061), Chaucer quibbles on queynte as (a) curious, odd, arcane, and (b) female pudendum (cognate with cunt); at Miller’s Tale 3276–77 he uses these two meanings separately, rhyming the word with itself. Queynt is also a variant reading for quoniam or quonyam in the Wife of Bath’s boast.

Solution 2:

Many sources (e.g., here) argue a tight connection between visual similarity of various foods to genitals and the aphrodisiac effect thereof; some even claim that the visual similarity sourced the popular belief in the effect.

One of the most notorious examples is the oyster: across ages and cultures, it is believed to be an aphrodisiac, among other things, because of the visual resemblance and the many alluring connotations of the shell.

This must have been on Shakespeare's mind, too, I think, when he cheerily put

Why, then the world ’s mine oyster,
Which I with sword will open.

into The Merry Wives of Windsor.

By the way, a feminist view of why it is awkward to find just the right term for an occasion is offered here. Further inspiration might be found there, too. Muff, for example, appears to be attested from the 1690s. Not mediaeval, of course, but still with a reputable history.

I do hope I got the gist of the question right. When saying female reproductive organs, you weren't thinking about the ovaries, were you?

Solution 3:

Fear not using the word cunt, since it was not considered taboo in public speech until 15c.

cunt (n.) "female intercrural foramen," or, as some 18c. writers refer to it, "the monosyllable," Middle English cunte "female genitalia," by early 14c. (in Hendyng's "Proverbs" -- ʒeve þi cunte to cunni[n]g, And crave affetir wedding), akin to Old Norse kunta, Old Frisian, Middle Dutch, and Middle Low German kunte, from Proto-Germanic *kunton, which is of uncertain origin. Some suggest a link with Latin cuneus "wedge," others to PIE root *geu- "hollow place," still others to PIE *gwen-, root of queen and Greek gyne "woman."

The form is similar to Latin cunnus "female pudenda" (also, vulgarly, "a woman"), which is likewise of disputed origin, perhaps literally "gash, slit," from PIE *sker- (1) "to cut," or literally "sheath," from PIE *kut-no-, from root *(s)keu- "to conceal, hide." Hec vulva: a cunt. Hic cunnus: idem est. [from Londesborough Illustrated Nominale, c. 1500, in "Anglo-Saxon and Old English Vocabularies," eds. Wright and Wülcker, vol. 1, 1884] First known reference in English apparently is in a compound, Oxford street name Gropecuntlane cited from c. 1230 (and attested through late 14c.) in "Place-Names of Oxfordshire" (Gelling & Stenton, 1953), presumably a haunt of prostitutes. Used in medical writing c. 1400, but avoided in public speech since 15c.; considered obscene since 17c.

Etymonline

Solution 4:

If you are looking for a word that is neither too clinical nor too raunchy, the word sex can be used as a euphemism for genitals, male or female. Womanhood can be used if you want something specifically feminine. Both of these are often used in the more explicit kinds of romantic fiction.