How funny....I thought my grand father had made this up too. I had never heard anyone else say it.
Our verson is different again..
Once in china there lived a funny man
His name was Chickeracker Ching Chine Chan
His arms were long and his legs were short
this funny man could laugh nor talk
chicderacker ching chine o cocker law rum
Boom tiddy or rum
willy willy wack

I think that my grandfather changed the Walk and Talk part because is brother had lost a leg in a Prisoner of War Camp...

My grandfather was from Kent England...
All our family and cousin were taught this as soon as they could talk.