Your sweat could be getting a bit of a current going through it, are there charging contacts near the part of the watch that gives you the rash? Salty water (sweat) and electricity could well be making acid that's causing the rash. Sorry that this isn't really a solution but I find if I don't wear my fitness watch when exercising I don't get rashes.
No, the Apple Watch uses wireless charging so there aren't any exposed contacts that I can see.
There are accessory contacts inside the strap latch. It's possible, though unlikely, that sweat is getting in there.
I had a fitbit back in 2014 and the irritation turned me off of all fitness trackers
In 2019 I got an Apple Watch with stainless steel band and have not had any issues
I had irritation during the first few weeks of wearing my fitbit charge hr but being a bit more diligent about washing it made everything go away.
On which part? Under the watch or the strap? I had a problem with the strap (I sweat a lot) so I got a Nike fabric strap - it breathes a lot, so no effect on my skin.
It should also be noted that there are two types of metal finish on the watch: the aluminium and the stainless steel.
Which version did you try? That is to say, what metal and which band?