Barry, I love that song, but the version I've got (on 'Songs and Rummy Conjuring Tricks') doesn't have that verse.

Yes, pate is the head. According to the Oxford Concise 9th ed., it's "especially representing the seat of the intellect". I'm sure the song uses it more colloquially than that - the old sailor is just glad to have got away with having his arm shot off rather than his head!