One of my very old fake books shows the Johnny Mercer composition as ©1936 Leo Feist, Inc, NY, with a rnewal ©1963 Leo Feist.

The first copyright may indicate when the song was originally released, which may help with searches.

While "borrowing" from older, and often more serious, songs was fairly common, that the song was "poking fun" at anything may overstate things a bit. The song is quite typical of stuff that was popular in that era, and references to how "civilization" was invading the old West were fairly common. Remember too, that in that era most of the songs were targeted at the Broadway (and/or movie) audience back in "New Yawk Sity" so few of them are likely to be - or be based on - real "trail songs."

You might find something on one of the several thousand possible variant spellings of the "tag line," "Yippy Ki-O, Ki-Aye" although hits probably will be pretty iffy, as the published music of the era showed lots of "imaginative" variants.

Assuming you've got the Mercer lyrics, often a search on a few "distinctive partial phrases" is more fruitful than just looking for a title.

John