My Mum's version, which I now sing to my children is:

In China once there lived a man
Whose name was Chicker-racker-ring-chi-chan
His legs were long and his feet were small
It's a wonder he could walk at all.

Chorus
Chicker racker ring chi chan chacker rorum
Pon my orum ecki pecki wan
Oh ko oh ko chicker pa chicker pa
Chicker pi chicker pi she en ko

They marched him up to the top of the hill
And they rolled him down with a right good will
They rolled him here and they rolled him there
The chinaman with the turned up chair.

Repeat chorus!

No idea how to spell it, of course, nor where it comes from (which was why I googled it in the first place) but there you go!!