That's cool - I've never heard the Chad Mitchell Trio do it. Glad to see I'm not the first to think of it.

By the way, the lyrics above are missing my favorite line (the way I learned it):

Ye haven't an arm, ye haven't a leg, hurroo, hurroo (2X)
Ye haven't an arm, ye haven't a leg,
Ye're an armless, boneless, chicken-less egg
Ye'll have to put with a bowl out to beg.
Oh Johnny I hardly knew ye

pax yall