Agree to take a second look and research the 12-ga. Also remember that an autoloader soaks up a bit of recoil to operate the action, even when all you use it for is singles, like in trap.
There is a MUCH greater variety of ammo for the 12, including very light target loads.
But the size/weight of the gun may greatly matter. While a buttstock can be cut and a nice pad installed at any length of pull, the distance to a pump action's foregrip may be an issue. A lot of current models have a longer one that comes closer to the action, so pay attention to that if needed.
And as a general safety reminder for the benefit of anyone that reads the thread, always remember to keep 12- and 20-ga shells separate from one another so that the person with a 12 can't accidentally grab a 20-ga shell. It can lodge in the barrel and, well, you know the rest.