... and Azizi, I agree fully with your suggestion that the cockney version might well have derived from a visit by Dan Emmett or another such troupe in mid-C19: they were very popular with all walks of life, and the cockney kids' variant might well have developed from the gray-cat/white-cat of slavery-resentment-minstrelised days. But how, alas, as you say, can we KNOW? It is all bound to be a bit speculative — which, come to think of it, is all part of the fun...