Above I cited Frank Tod, Whaling in Southern Waters as a book containing New Zealand whaling songs. It does; there are about fifteen. "Wellerman" is not among them.

But I have a truly interesting prospect based on something it says. It cites a book by an historian named Herries Beattie called The First White Boy Born in Otago, the first edition of which was published in 1939 -- but with several later editions, based on Worldcat.

The "First White Boy" was a young man, Thomas Baker Kennard, born May 6, 1841 at Tumai near Waikouaiti. If I read Google Maps correctly, this would mean he was born ten to fifteen miles from the Weller Brothers whaling station at Okatou. This would be after the Weller Brothers packed up -- but just barely after.

And Beattie quoted songs known by Kennard. One of these is the one listed in Shanties by the Way as "Whalers' Rhymes," elsewhere called "The Beautiful Coast of New Zealand." Another, called "The Whalers," I do not recognize based on the four lines quoted by Tod.

There is a copy of The First White Boy Born in Otago in the Library of Congress, but there aren't any that appear accessible to me. Nor have I found one for sale. But if anyone in New Zealand is still pursuing this subject, that might be a place to look.