Sentence structure of hoax and dupe

Those are resultative constructions in which the result is expressed by a prepositional phrase; they do sound natural, but they are either not quite idiomatic (the first) or not attested in the dictionaries (the second).

The first construction is extremely rare, and in fact I find nothing for "out" (ngram). The unique case concerns the preposition "off" and dates from 1799.

(ref. 1) I could have told her that Cyril had hoaxed me off the the field , but I was so chagrined that the […]

The second isn't found in dictionaries.

OALD, Merriam-Webster, lexico, Collins

However, the dictionaries (OALD, Merriam-Webster and lexico) attest the unique possibility of using a prepositional phrases introduced by "into"; all the examples (21) in lexico are of that sort. Nevertheless, the preposition "out" is attested in the literature; moreover, it appears that the usage is neither restricted to American English, although found a lot in the literature of that language, nor old, as show the following references that date from 2016 and 2017.

(ref. 2) She had duped him out of his position of Chairman and it still stung. He was a Magistrate, a man of learning, highly regarded in Bilston, yet this girl had ...

(ref. 3) Incensed that Blackbird had duped him out of The Great White Scot, he'd experienced something like a childish fit of pique and gone running to tittle-tattle ...

In conclusion, it can be said that the second verb can be used with "into" and "out of". As to the first one, following the author in reference "3" is a possibility that certain writers might find tempting.

Both exist but are not particularly common. I will start with the second which is more used than the first.

To dupe somebody out of something is not recorded as a set phrase in the dictionaries, but you can find examples with it:

It is alleged to have duped some 5,000 people out of as much as $40 million. (Collins)

This local police site says:

A warning has been issued after a number of elderly people were duped out of large sums of money after being contacted by bogus police officers.
Since 10 December last year to date 17 reports of courier fraud have been received by the force. With seven of those victims suffering losses of more than £135,000.

So the expression is used with the meaning of "suffering a loss by being deceived" and I found that it is used mostly in the passive and followed by a sum of money or possessions:

someone [a victim] is duped out of [robbed through deceiving] money/possessions

As for to hoax somebody out of something, it does exist and it is used in the same way as "To dupe somebody out of something", but it is even more rare.

The Daily Telegraph has an article quoted by Wikipedia (which is how I found it). It says:

Australia’s most notorious robberies: The day Qantas was hoaxed out of $500k.

But sometimes newspapers are not considered the most reliable sources, so I will provide another example from an English speaking author

Hoaxed out of our wedding presents by a girl who is not going to have a wedding at all. I miss my brooch. My throat feels naked without it. (The Honorable Miss A Story of an Old-Fashioned Town, by L. T. Meade)

So do they exist? Yes. Used mostly in the passive and followed by possessions. This GNgram will show you how rare they are, and that to be duped out of something is used more than to be hoaxed out of, which is probably due to the fact that "dupe" is more common than "hoax" as a verb:

It is worth noting that hoax is a word of English origin

1796 (used as a verb) "ridicule; deceive with a fabrication," 1808 (as a noun), probably an alteration of hocus "conjurer, juggler" (1630s), also "a cheat, impostor" (1680s); or else directly from hocus-pocus. (etymoline)

Hocus Pocus comes from early 17th century, from hax pax max Deus adimax, a pseudo-Latin phrase used as a magic formula by conjurors (OxfordL)

Dupe, however, is an even older verb of French origin. It was formed from the noun dupe around 1704, meaning

"to deceive, trick, mislead by imposing on one's credulity".

As a noun, dupe is dated in the 1680s:

"one easily deceived or led astray by false representations," 1680s, from French dupe "deceived person," from duppe (early 15c.), thieves' jargon, perhaps from phrase de huppe "of the hoopoe," an extravagantly crested and reputedly stupid bird. (etymoline)