My Mom's version was a little different but must be from the same original. It goes

Once in Japan there lived a man name Hiko-chiko-chickery-chan, Hiko Chiko chinaman, Wadame Kadame dusty-o willapy wallapy chineo.

One day the people of the town went up and brought the Chinaman down. Then the Chinaman he died and all the people for him cried.

And that was the end of Hiko-Chiko-Chickery-Chan, Hiko Chiko Chinaman, Wadame Kadame Dusty-o Willapy Wallapy Chineo.