As to the history of this song, I've started to go down the rabbit hole a bit more especially due to a note added recently by Robert Waltz of The Ballad Index.

When this song became an odd internet hit at the end of 2020, a number of commentators observed a similarity to a 1971 recording, "The Lightning Tree," by the Settlers. This is only a year and a bit after Neil Colquhoun reported collecting the song, and a year before he published it. The Tommy Wood recording is from about the same time. Colquhoun usually admitted to making up tunes when he did so, but could his source [...] Frank Woods have heard the song? - RBW

"The Lighting Tree" by The Settlers is performed HERE . Give it a listen, and recall the folk-pop atmosphere of 1971. This was the theme song for the U.K. TV Series _Follyfoot_, which first aired in June 1971. A commenter on this video notes (unconfirmed by me) that The Settlers' song reached #36 in the popular music chart that year. You might agree that the group, and their song, accorded with a "folk" aesthetic.

The idea that "Soon May the Welleman Come" may have been influenced by the _Follyfoot_ theme is not so far-fetched as it might first appear. Commence the rabbit hole dive...

"The Wellerman" bears the hand of NZ musician / songwriter / folkie "song collector" Neil Colquhoun, along, perhaps, with his collaborators in NZ's folkie scene. I can't speak to that scene. I wasn't there. However, a musicologist from Wellington, Michael Brown, who interviewed Colquhoun, provides history and context of Colquhoun's cohort. In a 2015 article in Journal of New Zealand studies, for instance, Brown writes (132-3):

//By the time _Shanties by the Way_ [a NZ song anthology] was published in 1967, “The Sailor’s Way” [a sea song] had already been “reconstructed” for live performance by school music educator Neil Colquhoun (1929-2014) and recorded by his group, the Song Spinners. This adaptation remains a popular item in the local folk revival under the title “Across the Line.”
The reconstruction of “The Sailor’s Way” as “Across the Line” included the creation of a new melody, which was apparently devised by Colquhoun for a schoolroom exercise using “Twinkle Twinkle Little Star.” ... New lyrics loaded with New Zealand place-names were also written by Delahunty and Colquhoun. Cowan’s fragment [referring here to a 1912 source] was thus transformed into a “New Zealand folk song.”
The degree of reconstruction required of “Across the Line” before it could be taken into the New Zealand revival repertoire was not atypical. As it happened, only a small proportion of the raw collected material satisfied both the collectors’ nationalistic expectations and orthodox criteria for folkloric authenticity.//

Michael Brown's piece on Mustrad in 2006 provides this information:

//Neil Colquhoun, an educationalist and school teacher (now retired), first began collecting local folksongs and verse in the 1950s. None of this material was recorded in the field, but rather learnt by ear or transcribed by hand. Cover picture - New Zealand FolksongsIn the late 1950s he formed The Songspinners, a revival folk group which played the songs he'd found, reconstructed or composed himself.

In 1965 Colquhoun published the collection New Zealand Folksongs (23 pieces) and in 1972 a much expanded 2nd edition New Zealand Folksongs - Song of a Young Country (51 pieces)... It is a populist collection and was principally concerned with presenting singable, 'complete' versions of songs. Many pieces had been assembled from fragments, amended or supplemented, both lyrically and musically, or were poems set to music. This approach did spread a positive message about the existence of a New Zealand folk tradition, but also aroused criticism in some quarters for its supposed inaccuracies. Perhaps most crucially, the collecting notes were extremely brief, which meant it was often difficult to know the nature of the original sources and the extent of reconstruction.//

So we get a sense of how Colquhoun may have worked with sources construct items of NZ folksong, including a liberal and practical approach of setting tunes and editing texts.

Let's take the example of an item "John Smith, A.B." A Twitter user from NZ has posted a 1904 Sydney _Bulletin_ printing of the item HERE

"John Smith" is supposed to have been a second item, in addition to "Wellerman," given to Colquhoun by his mysterious informant, Frank Woods. To me, "John Smith" looks like a piece of poetry; I'm skeptical that any performance of it as a song would have been part of tradition. I'd suspect rather that if anyone had sung it as a song, it would be their idiosyncratic rendering (however, I admit ignorance of the history of "John Smith"). Might the mysterious informant, Frank Woods, have presented this (sung it) as a song to Colquhoun? Or did he offer it in some other fashion and Colquhoun turned it into his own song? Here is Colquhoun's performance of "John Smith"— it may be compared to the 1904 newspaper text at the Twitter link above:
https://youtu.be/MBEH1-MuIp0

This performance by Colquhoun appeared on the 1971 album _Song of a Young Country_. That was the album that first (as far as we know) introduced "The Wellerman" to the wider world.

Not knowing more of the history of "John Smith", yet suspecting it was not a well-known item of folk tradition, only converted idiosyncratically into a song by either the informant Frank Woods or the collector-performer Colquhoun, we can become more suspicious of what either gentleman may have done in creating (*in a sense - more must be said) "the Wellerman."

More on this key moment of the first documented rendition of "The Wellerman" in a following post.