I would say stick with the gun he has and if recoil is becoming a problem, use less shot as suggested, or a lower velocity load.
Here again is where reloading can make a bit of a difference. Not only can you reduce the felt recoil by switching to a light powder charge, but you can also reduce it by switching to a slower burning powder to give you the same velocity and timing you are used to, but the duration of the recoil will be slower and longer and will not feel as hard as a faster buring powder that will be sharper and quicker.
By the way, I don't suppose your son is going to get any smaller, so that gun he has sounds about right.
Good luck on your search.