Physical Danger
The greatest physical risk comes from exposure to disease. Because you're a surgeon, you're opening up tissue and making yourself vulnerable to any infections your patients may have. Hence the mask and the gloves. You're not wearing them because they make you look cool, that's for sure.
You're also working with knives and scalpels and whatnot, so there's a chance you could cut yourself. But if you're so clumsy and unfocused that you're cutting yourself open rather than the person stretched out on your operating table, you may have bigger things to worry about than tracking down a butterfly bandage.