My daughter was a member of a synchronised swimming club for 6 years, and only stopped recently, as it was getting a bit much with her GCSE's. Once you are competing in a team it can take over a bit
There are no boys in her club, BUT I did see a number of boys over the years, competing at the Figure and Team comps, and doing the Grades etc. To answer a PP, they just wear swimming trunks - black at Figures and Grading, and sometimes colours/patterns to match team costumes at formal competitions.
It's tough, even at the recreational levels - eg: training sessions started with multiple lengths of the pool, - 3 crawl, 3 backstroke, side crawl with arm out of the water, sculling with ballet leg etc. There was a very brief 10 sec pause every 10 lengths. It was not unknown for girls to get out and stop as they felt sick! However, they all really enjoyed it, and the competitive element is great for building confidence.
Find a club he can join, and give it a go.