The person who laughs at their own mistakes first takes all the power out of anyone else’s joke.

A joke about you only works if you are defending the ground it is aimed at. Once you have already said the thing out loud, laughing, there is nothing left to expose, and whoever was lining it up finds their material has been handed over. That is not the same as putting yourself down. It is being first, and first is a completely different position.

Pick something small you are self conscious about and name it lightly before anyone else can. Watch what happens to the room. If someone is genuinely being cruel rather than joking, this is not your job to fix and telling someone is a reasonable move.