I now have a (borrowed) copy of _First White Boy_ (1998 edition; first published 1939).

No obvious Weller'sman song inside.

It does have (as expected) "The Beautiful Coast of New Zealand." All four of the verses that have been posted to this thread already, with only slight editorial differences.

They come in a chapter called "The Whalers" and under a subheading "Whalers' Rhymes."

The author says that Kennard,

//quote//
could recollect the singing of ordinary nautical songs of the type of "A Life on the Ocean Wave," etc., but he could remember hearing no chanties or special ditties. Someone, he knew not who, had composed several verses of doggerel about items topical of the day, and this used to be recited in a jocular manner. The first verse went:

Along the coast the Magnet came,
[etc]

[commentary on the lyrics]

Mr Willsher sold to Bloody Jack
[etc]
[commentary]

Waikouaiti and Molyneux,
[etc]
[commentary]

Peter Shavatt has a shocking bad hat,
And old John Hughes has shocking bad shoes,
[etc]
[commentary]

//unquote//

Commentary indicates knowing who these people were. And, of the fourth stanza, "The narrator says the second line should read 'Old Jack Hughes had Maori shoes,' according to the way he heard it when a child" (pg 32).

Kennard's father came to NZ on the brig Magnet arriving in March 1840.

TB Kennard was born May 6, 1841 at Tumai. Died Feb. 29, 1936.

No "Weller" in the index, nor use of that word in the Whalers chapter.