We've previously shown you a skit from 1966's Milton Berle Show with guests Adam West (Batman), and Van Williams & Bruce Lee (Green Hornet). In that same episode, West also performed a musical number. I believe the song is called, "This is The Life", as part of a skit that reveals that the captain's hat & jacket are just pro tempore as West is actually a deck hand borrowing "Captain" Berle's spare hat & jacket. Scope!
Like his contemporaries, William Shatner & Leonard Nimoy (Star Trek) and David McCallum (The Man From U.N.C.L.E.), West did release an album. Well, let's put it this way. He's got Shatner beaten already.