Just wear a pair of boardies on top. That's what most people do. My black billabong boardies go well.
I don't SUP surf so I can't comment, but a wetty at any other time would be hell. I used my (prone) surfing wetty once or twice when i first started SUP paddling as I didn't have any other option back then. It was the tail end of winter and I was still getting used to a race board too so there was a high probability of falling in back then.
Yeah, tights only would be tough to pull off anywhere.