My Watch

is disgustingly dirty.  I ran with it last night and when I took it off to get into the shower, my wrist was covered in black soot/dirt/something.  I had to really scrub to get it off.  My watch has been known to deposit some dirtiness onto my wrist before when I sweat a lot - found this out reffing, and it didn't really bother me then.  But wow, I was super grossed out last night.  I wonder if there is a way to clean my watch without submerging the whole thing.