When a mohel is present in shul, no one in the minyan needs to recite Tachanun.
If any reader is a mohel or otherwise would know how to answer this question, "fairly", I'm curious how often the mohel, himself, says Tachanun. Or, is it more common for the mohel to go to a minyan elsewhere where he's not doing a brit, prior to coming to the other shul where he will be doing the brit?