I'm very small. I'm 4'7" and weigh 73 pounds. Although I'm 19, I'm the same size as a ten-year old girl. So the recoil of a gun is important. It turns out that heavier guns kick less than the lighter ones. My favorite is a .50 caliber Hawken style muzzleloader. It weighs a ton, but I've learned how to hold the heavier guns and steady them for an accurate shot.

I have a 20 ga. NEF and it works fine for me, but I can't handle a
12 ga. Your son is a little bigger than I am, so can probably handle a bit more kick. Be careful you don't discourage him though by going too big and making him afraid of the gun or flinching when he shoots.