The only problems I've ever had with sweating is when my hands get a little sweaty and I can't grip the pick.
I'd drop about 10 picks a night.
Regular old fashioned Fender mediums.
Untill I switched to delrin picks.
Seems with delrin I get a BETTER grip when my hands are a little sweaty, and I like the sound and feel better as well.
Plus, I don't think you can wear these things out. I've been using the same one for months and except for getting a little shiny where I grip it, it shows no wear whatsoever.
But sweating is a part of life, and performing under hot lights is going to make you sweat. It's just something you have to get used to.
If it's very bothersome, or if you sweat like a fire-hose, see a doctor. They can help with that.
If it's not THAT bad, try some spray anti-persperant, yes, you can use that on your hands and you won't even know it's there.