The words sung by John Kirkpatrick to 'Not For Joe' were

There was a little nigger
And he got no bigger
So they put him in the Wild West Show.
He tumbled out the winder
And broke his little finger
So he couldn't play the old banjo.

'Om Si the Gom Si' can be varied to 'Umpsi Dumpsi Di-Do [3x] ~ playing on the old banjo!'. I always took this to explain the name of John's Umps and Dumps Band, on one of whose records [was it 'Among the Many Attractions of the Show will be a Really High Class Band'?] he sang these words.

All long ago ~~ all IIRC: except that I am certain I have remembered those words correctly.

~M~