If you don't want to go into flying a person to do it, you could potentially fly a marionette. Essentially, you would have the actor look like he was going to climb and then, through the magic of theater, be replaced by a stunt double/dummy (Buster, wherefore art thou Buster?). Would it look look as convincing as someone actually climbing? Probably not, but that's what the suspension of disbelief is for.