I think you are waiting too long. You should have two complete sets of shots before class. Waiting till they are 15/16wks you are missing critical socialization skills. Waiting for "all the shots" is pretty much old school these days.
My pups go out even before that to things like lure trials… you just need to be careful and not let them "get" into anything like "old poop" laying around.
I'm planning on taking her around the time of the 2nd shots if I can. But the problem is that the next round of puppy classes doesn't start till the last week of March, which would be around 14 weeks anyway. Maybe they will let me join the last half of the previous class but I'd have to check into that.