Perhaps it's a manipulation of "River Clyde"? To make it rhyme with "lady"? This song was written by Leo Maguire (whose son John I used to play music with on Tuesday nights) and maybe he employed some poetic license? I'm not sure whether "Claydee" appears anywhere in the song's many historical ancestors (no time to check right now) but even if it does, it could still be a contrivance of "Clyde".