The difference isn't in your arm... it's in the ballistic coefficient of the ball. Air resistance is going to slow down both the ping pong ball and the golf ball. Suppose a very simplistic model of air resistance, where the force trying to decelerate the ball depends only on the cross sectional area of the ball. That means that the air is exerting the same decelerating force on balls of equal size.
But the more massive golf ball slows down less, because it's more massive. The identical decelerating forces on the balls is going to produce a smaller deceleration for the more massive ball. On the moon, you could throw the ping pong ball farther.