I usually rinse between passes to reheat my skin and remove any stray lather that may have dried out on my face while shaving. It also lets me know any spots that I missed. I usually move my razor off to the side while I rinse.

No matter how careful you are, you will probably splash the razor at some point. Just towel the outside dry, run a q-tip inside the scales to get that water, and oil your pivot pin monthly and leave the razor open to dry for a few hours. Then you don't have to worry about it as much.