Generally the saltwater will actually help clean out a wound (particularly if you can get your cleaner shrimp to clean out the wound).
However, there are rare infections that marine hobbyists are prone to get from their tank. If you do get an infection on your hand/arm bad enough to go to the doctor, make sure that he/she knows that you raise marine fish. Certain vibrio bacterial infections and some atypical mycobacteria can infect humans from a fish tank.
In addition there is one sort of coral which gives off a toxin which can make humans sick if it can get into the body through broken skin.
That being said - I put my arm in my own tank as long as my arm is very clean. I am more worried about making my tank sick, rather than my tank making me sick).