We mounted a small box of soft shop towels in the race car that both driver and co-driver could reach. Then you have plenty of wipes for the visor. maybe even use Velcro to secure it and then be able to change it out at a pit if it is bad enough.
I'll second the clear safety glasses as long as they don't fog up on you. That way if you have to open your visor, you still have eye protection. The last thing you want is to lose an eye.
I've never thought about Jet Ski gloves, but that is a good idea. When racing a bike I used to get my grips and gloves wet before a possibly wet race to make sure that once wet they were not slick. Had to learn that one the hard way once, grips and gloves I was using were terrible once they got wet and I could barely hang on no matter how hard I squeezed, made for some wonderful arm pump in the mud.