There was a family version sung by all the womenfolk on my maternal grandmothers side to their children, I have memories of my gran and several of her many sisters singing at family gatherings.

The only verse of our version that I remember clearly went:

The Chinaman was very,very fat
and his servants they were very,very thin
They took him up to the top of the hill
and they rolled him down like a rolling pin!

Chicka Racka Chee Chi
Chan Chackalorum
Condolorum ecky pecky weck
Oko Coko, oochy, coochy, oochy boy
Itchi pie, Itchi Pie
Shee in coo