I didn't read all the responses so I may be repeating but...
My OB/GYN has been very understanding and he has teeny tiny offices. I do use a carrier but both of my sons were squirmy and crabby, so I would just take them out of the carrier and put them on my chest for some tummy time when I was on the table. No one batted an eye or thought it was weird.
The best part? The doctor and the nurses who got to see me through nine months of pregnancy then got a chance to see the baby (or got to see the baby as he grew bigger) and they seemed to enjoy catching up with the "end result".
Don't worry about it - just bring the baby in with you and if you can't hold him just say something like "Could I get a hand with holding the baby during the exam?" and unless they're not human, they'll say yes (and you know there's ALWAYS at least one person in every working environment who absolutely LOVES babies and will jump at the chance to cuddle/snuggle one up!).