I'm looking at all this (including referenced articles) for copyright considerations. (The question was raised.) Here's my personal summary (not legal advice - I'm no lawyer).

The oldest available lyrics were collected (amateurly) by Texas A&M professor Harris Braley Parks and published by the Texas Folklore Society, in a 1928 pamphlet “Foller de Drinkin’ Gou’d.” Parks gives details about having collected the lyrics from 1912 to 1913, implying they had to be much older.

The lyrics now known in folk music circles were apparently adapted from these Parks lyrics in 1947 by Lee Hayes of the Weavers. Lee Hayes said he learned the song from 19th century sources, but there's no supporting evidence to back that up objectively. Some of the recordings of his version credit the songwriting to a made-up name “Paul Campbell.” Most folk music enthusiasts have no awareness of the Parks version and consider Hayes’ well known version to be purely traditional, which it actually may be.

If the song is not truly from the 1800’s, then it's from the very upstanding H. B. Parks (1928) and/or the not-very-upstanding Lee Hayes (1947). But each of those two said they received the song from much, much earlier sources, essentially unidentified. They didn't claim authorship, and such a claim at this late date would seem implausible under the circumstances.

So it appears to me, for my purposes and from a layman's standpoint, that there should be no problem using any of this. And since there are no legitimate copyright holders from the last 95 years, crediting the song to “Peg Leg Joe” ought to be fine also, even though he has never been satisfactorily identified at all.