Hello,
I have some bunnies that don't like being picked up either - so the way I check their bottoms is to encourage them to stretch up so that I can see their tummies. Normally I do this with the use of a treat or part of their breakfast and they poke it through the wire at the top of their run or hutch so they stretch to get it. To them it's all part of the game. Obviously, if you have an elderly bunny who can't stretch like this, this wouldn't work.
Kindest Regards,
Sarah