You know, rather than speculation and assuming things can't be done without limbs (which is kinda hilarious that people are even making that assumption here), it wouldn't hurt to do a cursory bit of research.
Tisha Unarmed (who's been mentioned here before) has
a video of swimming without arms.
Or, you can go all out and refer to someone like
Nick Vujicic. No arms, no legs.
Vujicic gradually figured out how to live a full life without limbs, adapting many of the daily skills limbed people accomplish without thinking. He writes with two toes on his left foot and a special grip that slides onto his big toe. He knows how to use a computer and can type up to 43 words per minute using the "heel and toe" method. He has also learned to throw tennis balls, play drum pedals, get a glass of water, comb his hair, brush his teeth, answer the phone and shave, in addition to participating in golf, swimming, soccer, and sky-diving.
(And yes, I recognize that Wikipedia follows that up with "[Citation Needed]". There are youtube videos that I consider sufficient citation.)
As has already been pointed out, I've kind of explored the issue (to some extent) in the fanfic I'm currently writing. That's not so much definitive as it is one possible way things could be, of course.
All we know for certain (i.e., all that is canon) is that there is a pool, it's "for physical therapy" (in context, the "for physical therapy" may be an answer to "how is a pool official?"), and the nurse considers Hisao's heart care an acceptable use of the pool.
Considering the mission statement for Yamaku seems to be "as normal as possible," I would expect that there is more likely than not a swim team. By logical extension, there would be a uniform swimsuit. Whether or not it's
the uniform swimsuit is another question entirely.
Considering each of the girls and their relation to water:
Emi likely used a pool for physical therapy.
Rin could go either way, but that's pretty much par for the course for her.
Lilly isn't as interested in swimming as Akira (this is canon), but I'd tie that more to the fact that Lilly just isn't athletic in general.
Shizune (and Misha) could go any which way - it's never really touched upon for those two.
Hanako... is the interesting one. I imagine it would be uncomfortable for her, but not due to chlorine or anything like that. If she hasn't been in the habit of swimming, the new motions would likely to pull on the scar tissue, since it isn't as elastic as regular skin. After a while of swimming, that discomfort would gradually disappear as the body adapts. On the more obvious question of her comfort with wearing a swimsuit, it really hinges on how she sees herself. Does she think of herself as ugly and tries to hide because of that? Or does she try to hide because she knows others are repulsed by her appearance, and will use it as an excuse to treat her horribly.
In other words, does she hide her body because she dislikes it, or because other people dislike it? If the former, there's no way she'd get over that complex in the few remaining months between Hisao's arrival and graduation; if the latter, it's
conceivable she might
wear a swimsuit around people she trusts in a private setting. To reemphasise, this would be people that
Hanako trusts. At best, you could probably count those people on half a hand, and have fingers left over.
Miki, Natsume, Yuuko, Ritsu, Ikuno, Molly, Hitomi, and (presumably) Hachisame would probably have no issue other than personal hang-ups.
Naomi, Suzu, and Misaki
might have concerns if the condition is severe enough, and precautions would likely be taken, but I expect they could swim without much trouble most of the time.
