I agree with Kevin re singarounds. I don't see them as performing as such, especially amongst friends, but that said, your human nature alone tends to make you not wish to disappoint so the effect can be the same.
Many reading this probably don't sing outside of a singaround session anyway so to them, it's the same as a pro singer on a stage, trying to entertain. Two things spring to mind here;
The advent of the singaround as I see it these days differs from the folk clubs in that you aren't necessarily the object of attention. Many ignorant sods are too busy flicking through folders in the assumption everybody is just sat patiently waiting for their latest three chord wonder or melody that falls flat. Of the others, some are talking with each other and one of two?
They are listening. They are the only ones who count and they understand your anxiety and don't factor it in any way shape or form in their appreciation of your talent.
Oh and to bring the others back into the fold, nobody remembers your cock ups, nobody remembers that the intonation wasn't up to your usual standards.
If you are judged at all, you are judged on an amalgamation of everything they have heard you do, not tonight's faux pas.
Enjoy your music and hope at least some sat there do too.