My hot flushes are like that — hair damp like I just stepped out of the shower, sweat dripping down into my desk. Fortunately, they're rarer than they were a few years ago.

For me, the best answer is a fan: sit in front of one until you dry out. I also have a portable fan similar to this one, that I can carry in a satchel, backpack, or even the pocket of my cargo shorts.
https://www.amazon.com/Handheld-Portable-Operated-Personal-Rechargeable/dp/B086ZQMBLX