"Little Joe the Wrangler" as posted here by Stewie, and in the DT, follows Thorp's original fairly well, but there is a misheard word in verse 2 and a sex change in verse 4.
Verse 2- brogan shoes, not broken. I guess brogan shoes (a heavy shoe, reaching to the ankle) are seldom worn now.
Verse 4- Thorp original- Ma, not Paw, beat him.

He said he had to leave his home, his daddy'd married twice
And his new ma beat him every day or two;
So he saddled up old Chaw one night and "Lit a shuck" this way
Thought he'd try and paddle now his own canoe.

There are other minor changes from the original as Thorp published it in 1908.
See Fife and Fife, Songs of the Cowboys, pp. 28-32, and facsimile original (unpaginated) following page 237.