I don't know if they make 20's, but Aquila makes a low velocity shell for a 12 that my grandson, (age 8, 65#), shoots ok. They are about half the length of a standard shell, and I believe they were made for increasing the capacity of self defense shotguns, but they work great for this. If they make 20's that would be even better.
Failing that, put some weight in the stock, via a lead filled sock, etc. and that will minimize the recoil somewhat.
Hope the best for the small guy,
Ben