Extremely wet boy here. It's just how I've been since I was a teenager, my dad's the same so must have a hereditary component, but I have noticed it helps me keep cooler and skate a little harder for a little longer than some people who don't sweat as much. I live in the desert and get up at around 6 am during the summer months to skate, in large part so I can skate in 90 degrees instead of 105. Large bottle of icy cold water is a must. I wear a hat and and very light (and mostly open) button-up shirt over a tank or muscle shirt just to catch sweat and to be able to wipe my face on the sleeves. I have definitely considered wristbands in the summer. I'm burning up with or without the shirt, but with it there's something to keep the sweat from going all over.
I sometimes carry a spare shirt with me when it's unbearable outside because nothing else will work after a certain point. As for drying strategies, not getting damp in the first place is the best strategy, but in a pinch letting the AC in your car or breeze from the open windows blow up your sleeve and into your pits can be pretty quick.
At my college advertising job, there was a cute summer intern who seemed kind of into me. One time she asked me if I wanted to go up to the top of the parking garage and sit for lunch, so we did. It was really sunny and crazy hot, and I started to feel my pits getting sweaty, so I tried to put some air between my arm and body to keep things as dry as I could. Right after I did that, she noticed a single bead of sweat fall from my pit out of the opening in my sleeve and hit the concrete bench we were sitting on. She said "Wait, what was that, did you spit or something?" I just flatly said "No" and then there was a tense pause before we kind of haltingly talked for another 10 minutes until the lunch break was over. It doesn't sound that bad, but 20 year old me experienced it as a kaleidoscopic nightmare.
At my wedding (to a different woman) I fucking pit sweated through my undershirt, shirt, and suit jacket WHILE USING PRESCRIPTION ANTIPERSPIRANT. It shows in the wedding photos and everything. Knowing beforehand how sweaty I can get, my sisters tried to get me to put maxi pads under my arms before the wedding and I refused, either maintaining or sacrificing my dignity in the process.