All this seems very Anal to me !! Why the obsession with the who what when and where, its a good Tune and certainly old enough to be out of copyright, so why not just play it and enjoy it !!!.
If it does not muddy the waters too much, I know several east Anglian style musicians who play it under the name of "Little Pet Polka" Incidentally James Brown was an early Superstar of the Button accordion, from Glasgow I believe, who made recordings in the early 20th century which even by modern standards and the limitations of early recording, where virtuoso performances.