I have often threatened to acquire a (empty) guitar case to take with me to sessions, so then I know that I will then be asked to sing. We're down in Cornwall at the moment and hope to get to a local session on Wednesday, perhaps I have more confidence these days and will even ask if I can sing! However I'm still of the opinion that whoever's running the session should ask everyone in the room, even strangers, if they want to perform.
I often invite the people in the session to join in with me in songs, but that usually means singers, and depends on the type of song. Surely the best type of session is a mixture of 'all sorts'
I do find that as an unaccompanied singer I can vary the timing, volume etc. and hopefully share my version of the songs that I sing.
Carol