At last I can prove to everyone this song actually exists.
Albeit with, yet again, slightly different lyrics.

So, as sung by my maternal grandmother in Belfast:

There once was a little Chinee man
His name was Mister Chikalaka Brown
HIs head was big and his feet were small
The poor wee man couldn't walk at all.

...Chikalaka Chikalaka Chang Chikalorum
Chang Chikalorum Allaallawack
Hoko Poko Sock him in the Boko
Itcheeko Itcheeko E I O.

Ring any bells?