Being from Arkansas I've killed several whitetail deer with squirrel shot when I was a kid.
For HD I would pass on the low brass birdshot but if you are concerned about overpenetration of BS in your house, trailer, apartment, condo, etc and high brass #6,5 or 4 shot will do the trick at short distances, like the ones you will deal with inside your home.
At 20' a high brass squirrel shot is still a solid mass even out of a cylinder bore and will punch through stuff just like BS but will break up while going through a standard sheetrocked 2x4 wall.
I have a Win 1300 Defender for HD and even though the tube holds 7- 2 3/4" shells I only load it with 5 plus one in the chamber. I also have a 5rd shell holder on the buttstock that's loaded with 3 "OOO" and two 3" 1 1/4oz slugs.
For the "what if" guy....... Load you shotgun with 1 round of squirrel shot in the chamber and 5 rds of SS in the tube and 3 rounds of BS and 2 slugs in the shell holder. Or place a SS in the chamber, 2 BS in the tube, then 3 SS and BS and slugs in the shell holder.
Since I live with just myself, the Wife, a dog and a cat I'm not too worried about shooting someone at the other end of the house and my nearest neighbor is 300yds away I use BS.
When I lived in a condo with my daughter I used the SS/BS combo that I posted.
If you blast a BG at 15' with a 2 3/4" high brass #4 squirrel shot load in his COM he will be dead by the time you can walk over to his corpse.