I'm not a naturally outgoing person and although I would be happy to do something behind the scenes, I'm dreading the public ordeal of being on the stocks. Can I get out of this without seeming churlish and uncaring?
I don't like the sound of this. Your boss must know you're not an extrovert and I bet that's exactly why he's fingered you for this particular ordeal. If I'm right, this marks him out as a bit of bastard; you'll know from other evidence if that's the case.
Despite all the above, and if you can possibly bring yourself to do it, I believe you should. It won't be (can't be) quite as agonising as your fertile imagination projects and you'll deny him the satisfaction of seeing you funk it. And when it's all over, you may even feel a certain inner satisfaction.
But if you really, really can't (which would be utterly understandable and not in the least shaming) you should politely refuse, but volunteer to undertake another task at the fete which, if not as exposed, is at least as arduous and time-consuming.