Good suggestion Philmo! I went into the sea in a wetsuit just yesterday. (I have long hair but am not a young man with bulging muscles.) Re self-consciousness, I get the problem but you do just have to tell yourself the truth, which is that No-one Else Cares. Even a tiny bit.

I went swimming in a pool fairly recently, and it turned out to be "women only night". I had previously had the impression those are a fairly new thing mainly due to demand from Muslim women, and indeed there was one Muslim (I assume) woman there, having a 1-on-1 novice swimming lesson in a burkini, if that's the word, but also lots more very overweight women than you would usually see. I wondered if they would usually have been put off through self-consciousness and felt more comfortable in this all-female session.
-N.