I'm not sure how much a 20 would "handicap" him. If the 12 guage is to much gun for him (a distinct possibility for a 12 year old) then he's probably going to flinch every time he pulls the trigger and that's a much greater handicap.
My wife and I shot trap for 30 yrs. She shot for Beretta for a while and they gave her 2 301’s - semi-auto. We cut the stock to the bolt length and put a pad on it. She sold more 301’s for Beretta than you can count because people would see that 5’2” girl out there shooting 400 competition rounds + practice every day for a 3 day weekend. At the Grand American shoots we would shoot 1500 12 ga. trap loads in a week.
Most of the women and kids that get hurt from recoil are because the stock is too long. The manufacturers make them long so they will fit the largest men and then you can cut them down as needed and add a recoil pad.
Get a 12 ga. semi-auto instead of fixed breach like an 870. Then shorten the stock to fit.
Good luck!! It’s great fun!!
The handicap would be that they don’t make a 20 with trapshooting stock dimensions.