Hi, Yes I too am surprised all the versions of this rhyme
I learned as this ......

There was chinese man
and he grew so tall
He could not walk and he could not talk

We took him to the top of the hill
and rolled him down with a rolling pin
and he said...
Chick a racka
Dona racka
Che chi cho
Chicka rollo bungalow
piggy wiggy wag -o-

hoko poko
hit him on the coko
it-a by
it-a by
che chi cho

I was taught this from my Grandmother as a child and have passed it down to my children.