My Dad used to sing this--he learnt it from his mother and thinks she learnt it from her parents, so we are going back to mid-late 19thC Lancashire:
Once in China there lived a great man
and his name was Chicker-ricker-rookington
his legs were long but his feet were small
so that Chinaman couldn't walk at all
CHORUS: Soooooo--chicker-ricker-roo chy cho chucka-larum
Scandal-arum is a peg man
Cargo too-go is a giz gaz go
is a peg nay go
is a peg man
Cheero cheero chuck chucka largo is despatched in China
here he comes and here he goes
the Chinaman with a monkey's nose

Two smart men they carried him about
the people did laugh and the people did shout
they took him to the top of the hill
and rolled him down like a rolling pin (sometimes changed to 'beechams pill'by my mother, an English teacher and purist about rhyme
CHORUS repeated

I've never found anyone before outside of our family who had the remotest idea about this song, which we figured must have come into the family from trips to the old music halls--unless anyone knows of any sheet music for it?