Yes, it is very disconcerting to follow a brilliant singer but its worse if they sing a song in the sort of thing you tend to you do yourself. But no matter how good they are, I, you and every individual is unique and can contribute something a bit different to a singaround. I agree with Lady P that the key thing is to sing something in a different style.

Perhaps Don't mind the wind nor the rolling sea ... followed by I like to rise when the sun she rises ...
Alan