Oh, dear. Well, that's a great way to wind down the day! I'd suggest getting a new meter, letting the soggy one dry out a bit, then compare readings between the two. It's a good idea to have a spare meter, anyway... and spare batteries, too.
I guess by now, everything turned out okay for you. Whew! Just want to add, here, that if it was my situation, I wouldn't shoot without checking, first. Of course, if you know your cat well enough, doing so might be safe enough. Your call, but I'd rather be safe than sorry.