Arguably, most surgery would be Pekuach Nefesh and therefore the risk acceptable since if the surgery works well there would not be Tumah and would save a life. A bigger problem may be (I have heard various things over the years) that modern medical training normally includes significant work with cadavers.

@manasseh There's a number of surgeries where not performing the surgery would not lead to a loss of life (ex. cosmetic, dental). Additionally while many situations may at some point well down the line cause a threat to life, at the time of the surgery that's only a possibility (ex. internal inflammation, or stones which require surgical removal; they could become infected, but maybe not).

@DonielF On the other hand, many of those same ones that are not Pekuach Nefesh - e.g., dental - would have such a minimal risk of death to be insignificant. On the other hand, there are other factors too - e.g., a modern large hospital is a place where even if you are simply visiting people you have a risk. My previous Rabbi was a Cohen, but he would visit the sick in hospitals anyway, but would leave quickly if there was any indication of a Meis. (FYI, I am a Katz but not a Cohen.)

To be clear, pikuach nefesh trumps the prohibition of being near a dead body. Is the question only about surgeons who don't deal with pikuach nefesh situations, or about choosing to do something (study) that will cause you to be called on to help in pikuach nefesh situations more often?

@AA If the Kohen is already a surgeon, I could hear the Pikuach Nefesh argument. But does that apply to a Kohen deciding his field of study, in order that possibly decades down the road he might save a life?

@DonielF I'm not sure I follow. Deciding to learn something can't be prohibited. If it turns out later that he is best placed to save someone's life, great. Are you asking about doing surgery while in training and he's not really needed to save the life? That's kind of the same as the general medical school training question (resident's working on shabbat, for instance)

@AA I guess my question boils down to may one initially put himself in a situation where this problem may occur later on because of his original decision

So "may a kohein who is already a doctor study a surgery technique which is not used in pikuach nefesh situations"?

@AA Yes, but which may still lead to tumas meis.