Actually in my experience the normal practice in sessions is for the question of who wrote the song only to come up after it's been sung. "Whose song is that?", or (for recidivist somg writers) "Is that one of yours?" The question normally only comes up if someone likes it.

I suppose, if someone says "That's a bloody awful sing", the thing to do is to say "Well, it's not one of the best Bob Dylan/John Lennon/Ewan MacColl wrote, I grant you, but I thought I'd sing it anyway..."