During the shave I rinse off my blade, after the shave I rinse and then wipe. I find rinsing easier than having to wipe, set the lather/hairy mess down, pick it up, move to a clean part, do it again. Some guys in the past posted about wiping off the razor on one of those beer can insulator things, which sounds like a good solution - wipe, turn, repeat and rinse it at the end of the shave.