Not to take away from Clint's swimming skill, but according to the original news story, he and the pilot first got out of the wreck on two inflatable rafts. Later, apparently at the breakers off the coast, the rough seas tossed Clint off his raft, and he had a harrowing swim the rest of the way in. The sea is a bitch.
You can read more about it, including text from the original 1951 news story, in this San Jose Murk article about the modern attempt to find the plane.
Or, rather than giving the Murk a hit, you can read the article directly. (Ah, if this image post from FastCompany's servers works...)