Not sure if it's helpful, but I use physio tape. I bought some when the physio showed me how to strap my foot. But I have load left, there is no way that sweat would make this stuff peel off, in fact getting it off again is the worst bit. I have to take it off in the shower and have even left it on for a few days when I wasn't brave enough. When taping joints the physio uses some other tape underneath to "protect the skin" which shows how sticky it is.
*disclaimer - I'm just saying what I use, please don't blame me if you rip you nipples off trying to get this stuff off. I bought mine from physiosupplies.com or some similarly named website.