I can't believe I found this. My grandmother used to sing it to me and I have never met anyone who knows what I'm talking about.

Her version went:

In China once there was a great man,
His name was Chickery Choo Chai Chan,
His legs were fat and his feet were small,
That China man couldn't walk at all.

Chickery Choo Chai Chan-galora,
Bang-alora, Men-a-Kin-Men.
Lang-con-do-dee
Idi-kiddi-pi!
Idi-kiddi-pi!
China Coo!

My god, it is quite insane when you write it down. The Idi-kiddi bits were inevitably accompanied by a burst of tickling.