Depends where. I do it on my face, because fuck extra irritation to my skin. Wife does the same with more delicate parts as well.

But, if im sweating enough to need to keep dabbing my face, I'm tying on a bandana (which I always have at least one of unless I'm in the shower).

In the gym, which is where I'd use an actual towel rather than something like a bandana to dab, I would still dab my shoulders because they're too damn sensitive as well. I don't go shirtless in public though, so I dunno if I'd just dab everything else as well out of habit, or if I'd wipe.

Honestly, my pale, partially irish ass doesn't go shirtless outside at all; nut even in my own back yard, back when I would mow, I was prone to letting sweat do its job as long as it wasn't getting in my eyes. At the gym, wiping down or blotting is an act of decency, not dripping everywhere. Sweat keeps you cooler if you let it stay and drip. Not by a ton, but it helps when you're in the south.

But yeah, you just haven't run into people with sensitive skin that were also sweaty.