Sweat damages almost anything. The salt and the moisture over time eats through even metal. The reason for putting your camera and lens in dry boxes is to reduce the moisture which will encourage growth of fungus. Sweat seeping into the camera?? I think you need more than a dry box to salvage the situation.
I sweat a lot during outdoor shoots too, so I would always bring a towel along. You could also do what some racket players do, buy a wrist band to stop the sweat flowing to your palms. My 2 cents if that helps.