Most docs just use a spatula when doing a pap during pregnancy, instead of the little brush. It's pretty much a waste of time, because the spatula doesn't get enough cells to get a good reading. I think I'd be fine skipping it, if I were in your shoes.

Geeky is right...refusing something routine and seeing their reaction to it will give you a good indication of what this team of attendants will be like in late-pregnancy and labor. Better to find out now how pushy they are.