I would be more worried about magnetic fields then x-rays

Other then causing them to GLOW in the dark I see no reason that x-rays would effect the watch or the handheld, a strong magnatic field maybe but it would need to be pretty strong,,, I spent a good soild 90 mins mounting a pair of sub in the back of my car wearing my watch cell phone and Ipaq with no issues and those speakers warped my tv screen from 10 foot away. (odd colors in the corners you know what I am talking about it goes away when you move the magnets)