There are a lot of lower recoil 12 ga choices out there. Simply picking a lower weight shot charge, lower velocity etc will go a long way to reducing felt recoil. I suspect that pretty much any size shot will get the job done as the shot pattern is going to be pretty tight at any likely indoor distance.....think softball sized pattern.....How much difference in recoil is the 12 ga SW vs the 20 ga? i have a 12 ga and wife don't like it but i don't own any 20's except my Savage 220 Slug, thought about getting a 20 ga SW.
Personally, back when we still had kids at home and wall penetration was more of an issue I used a combination of frangible .45 loads in the pistol and a Mossberg 835 with the first few shots being #4 shot followed by a couple of 3.5" Hevi-Shot #2s.