Apparently Dylan learned the tune from Canadian Folk singer Bonnie Dobson's version of "Peter Emberley" (Northeast/Maritime/Atlantic Canadian folk ballad about a Prince Edward Island lad who dies in a New Brunswick lumberyard accident).

"Emberley" usually has a distinct arrangement/tune that I wouldn't feel comfortable calling the "Tramps and Hawkers" melody. It's similar but not the same. Yet, Dobson mixes the standard "Emberley" melody with the "Hawkers" melody, especially in the first and last lines. Dylan is supposed to have written that rare "Donald White" ballad using the melody and later recording it with the "I Pity The Poor Immigrant" lyrics.
https://www.youtube.com/watch?v=SAzBpHtzXnQ

Interestingly, there is a second and rare Prince-Edward-Island-Boy-dies-in-lumberyard song entitled "John Ladner". This man died in a Maine lumberyard in 1900 and his body sent back to PEI to be buried. Ladner is buried in little country cemetery where some of my family and friends are also resting. "Ladner's" melody is "Tramps and Hawkers" (in all the versions I've heard thus far).

"John Ladner" seems never to have made the acoustic guitar folkie evolution. The only recordings I have heard or can find were done by folklorists Louise Manny and Edward D. Ives in the 1940s-1960s. These are from unprofessional, mostly retired labourer senior citizens recorded in the field and have never (or rarely) been published.

As you can hear from this 1947-48 recording of "Ladner" by Stanley MacDonald from the Louise Manny Collection, it is the "Tramps and Hawkers" melody. No one knows who wrote the words but it must have been a chum from Maine who knew Ladner well.
https://www.youtube.com/watch?v=EUyLesf-9QE

Edward D. Ives wrote an essay about the song that I'm looking for and may contain more info but this is an interesting instance of the melody usage in the Northeast of North America.