Get in the cage, turn the L Screen around so the tall end is to the right (for right-handed dads/moms), dump the balls on the ground beside you, sit on the bucket behind the screen, and toss underhand from about 15' away. After you release the ball, get the right arm back behind the screen. Quickly. This is how my sons' college team does it in the batting cage so it's really not a concession to a lack of arm, reflexes, and vision on my part.
Years ago I bought a full set of catcher's gear, sized for me, but when you feel like they're really gunning it, on perhaps their third warmup throw, time to go...