well... it sounds pretty serious if he's got to keep his leg straight while sitting down.
I have a friend who lost a TON swimming. She was never comfortable, and still isn't, peeling off her clothing in front of any one, and instead of popping into a bikini, or even a full one piece bathing suit, she has swimming 'pants' Her swimming gear looks more like a wet suit, and covers her pretty much entirely.
Finding some form of exercise he can do for his own health is important, but it is not essential to his weight loss.
If his obesity is stopping him from doing these things, then the focus of his attention almost has to be his diet.
Now.. I find myself able to do almost any exercise I want. I can hang on the elliptical trainer for an hour at a time, but modifying my diet is the tough part for me. It's tough to change eating habits, but can be done.
I'm in favor of diet control and exercise for healthy weight loss, nevertheless..people can lose weight without exercising, and that's what he needs to do.
Losing the weight will not only make him less self-conscious (so that he's not so sensitive about peeling down for the pool), it will make ALL forms of cardio more attainable for him. It will reduce the stress to all his joints, and make life less painful for him. And it will reduce the stress on his heart as well.