Hmmm....here's another example of a bike that the frame number indicates a late '56 or early '57, but was purchased in '58 (did grandpa buy it new, or maybe slightly used?). Your bike is 43 units later than mine (15249).
I think if it was mine, I would refinish the wheels & leave the rest alone. Don't be surprised if you find that the races & bearing cups need replaced. Also, take care when removing the drive pulley from the rear wheel. They tended to rust where moisture & dirt collect between it and the rim.
Mike Sal