Swimming for exercise!
I've been swimming for years so that lessens the worry about being the fat one the kids point at - somewhat. Luckily, the people at my health club pool are very encouraging. Plus in this world of political correctness, most kids are taught not to mock others. The worst humiliation I felt was years ago when a very concerned kid asked what was wrong with my thigh? Nothing just cellulite... Argh.
I walk with a cane and can't walk on hard surfaces, so I wear my flip flops going down the steps into the pool, holding the railing in one hand and using my cane with the other hand. Then I leave my cane and flip flops at the side of the pool. If you are self conscious, do the same with a tee shirt. Or wear a rashguard.