The biggest problem with contamination is the strap. It's easy to clean a watch with a rubber or plastic strap, and easier still with a steel bracket. NATOs and leather straps -- anything porous -- will be difficult to disinfect. I shower with my watch on, and if it gets too funky I'll clean it under the sink with dish soap.One of the worst things medical staff can do is wearing a wristwatch, because in all these little gaps there is a lot of space for bacteria and other germs. This is the only watch I know to be sterilised. I don't want to have the surgeons Rolex in my abdomen...
Edit: There is also the St. Gallen Horology desinfactable series.