Do we know how long Bostonians have been given that nickname? & was a 'Big' ever appended to it? & did it mean they were dogs [acc to OED, the term 'Bow Wow' for the noise a dog makes long preceded any written record of its being used attributively to mean the animal making it - dogs said 'Bow Wow' long before they were actually called 'Bow Wows'] in any figurative sense, or just people liable to make loud noises?

I agree it is clearly a nonsense chorus, rather than one in which the Bow-Wow element is appropriate because the song is about dogs, like the broadside cited above: but the 'Big' does seem, as you say, to connect it with Aird & Scott. But I remain intrigued why, nonsense chorus or not, it goes with the Aird/Scott 'Big Bow Wow' motif, rather than with the equally available & much more widespread simple 'Bow Wow Wow', which would fit the rhythm just as well.

Don't suppose we'll ever crack it at this time of day, mind; but I remain intrigued.