My mother sang a version of this nonsense song to me as a child in the 1960s :) Obviously it exists in myriad forms. Here is hers:

Chickarackah choochai chang chickolorum
Boomtahlorum waddy waddy wah
Oko Poko hit him on the iddygo
Tiddywa tiddywah sheepeecoo

In old Peking there lived a funny man
His name was Chickarackah choochai chang
His arms were long but his legs were short
Poor Chinese couldn't walk or talk

Chickarackah choochai chang chickolorum
Boomtahlorum waddy waddy wah
Oko Poko hit him on the iddygo
Tiddywa tiddywah sheepeecoo

His parents used to carry him about
Upon their back where he could shout
Here he comes and there he goes
The Chinaman with the big fat nose

Chickarackah choochai chang chickolorum
Boomtahlorum waddy waddy wah
Oko Poko hit him on the iddygo
Tiddywa tiddywah sheepeecoo