My mom is 88 and I'm 62. I remember her singing it to me when I was a child. To the best of my recollection it went:

In China once there lived a man
His name was Chickety Chickety Chan
His feet were long and his toes were short
And this is the way the Chinaman spoke.

Oh. . .
Chickalee chall-I chall-o
Chickalo romeo in a bananago
Alago walago chanticlee
In a bananago out you go

Oh. . .
This poor Chinaman he did die
And in his coffin he did lie
They shipped him back to old Japan
And this is the way his epitaph ran

Oh. . .
Chorus