is it ok to inhail fire extinguisher dust?
Anywhere you could mount it, the camera would still have a chance of getting hit by a stray shot (unless some sort of protective case was built around it). Also mounting it on your mask wouldn't work well because you couldn't see anything with the camera. No matter where you mount it, you will have a huge amount of shaking and watching a video of a paintball game like that would just give you a headache. Your best bet for recording a woodsball game would be to have a seperate person, with appropriate safety gear, record the game with a video camera as digital camera's video recording capability isn't great.
You have a reason to be worried. Gloves are required, especially since AIDS has become so well known. Complain to the hospital about this nurse.