There are groups where you won't get a chance to sing unless you have a guitar.

The remedy of course is to get a cheapie guitar at a yard sale or flea market; sit in the circle and be ready; when your turn comes; hold the guitar as if you are going to play it; then pointedly put it down and stand up and sing.

That way you will get your turn and the more intelligent ones in the circle will understand that it is deliberately unaccompanied.

I don't know what you can do about the guitar hogs though, because they are so thick that nothing short of a two by four alongside the ear will stop them.