Im not sure 20 ga comes in anything but #3 buck or some slug.
20 gauge is my primary HD gun for a bunch of reasons but as to what is available I just checked my inventory and I have #8, #7 1/2, #6, #4, shot. 4 buck, 3 buck, 00 buck shot plus SST slugs and FTX slugs. I'm sure I don't have everything but I guarantee you can get 00.
Because of the people in my house and the way my house is laid out I use #4 shot but your situation may be different and you have to make your own choices but gimmick rounds isn't one of the choices. At 10' that rubber ball is as lethal as anything you can shoot out of a shotgun barrel. It was designed for crowd control and they were thinking 50' + not up close and personal.
For SHR970 with the 5" hole at 10' you might want to check your choke. At 10' I put a hole through a 2X4 just big enough to stick my thumb through using #4 shot and an IM choke. at 8 yards I have your 5" pattern and 8 yards is the absolute longest shot I could make in my house, figure most SD shots would be less than half that.
Comment on the light was for the portable light, I have a night light in the living room, and the kitchen and the front porch plus a light on a motion detector on the garage. All of those can be bypassed by pulling my meter and the house is dark but my maglight on my nightstand will still work. I live in the sticks and a car accident with a power pole or a lightning strike on a transformer can put me in darkness for 3 or 4 house easy. Porchlight won't do me much good then but one of my maglights will always work.