The area is not all high end and classy. Not at all. Maybe a hotel here and there in Bellagio, or in Menaggio, but once outside of those few hotels, go swimming in your running shorts, wear a T-shirt and flip flops (not that Italians dress that way on vacation), and no one will care.

No dress code. Feel free. It's not snooty at all, outside of a few super high-end hotels. No worries at all. As for water temperatures, not sure what to say. Probably warmer than going into the water at a beach in LA. The water is not cold. Jump in, swim around, feel fine in a minute or two, especially if it's hot outside on that day. It's not a cold lake in the summer.