Having never seen a man cover his hair with a kippah while swimming I always assumed it was permitted to do so. However I am curious if there is any halachic discussion recorded which explicitly permits a man to swim without a head covering.
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Yes there is discussion, and since this is Judaism we're talking about, there is of course disagreement.
The Kof-K has a document (PDF) regarding the wearing of the kippah, which footnotes numerous sources for the following sentence:
It also quotes several sources that are stringent. You may wish to CYLOR.