It's been my experience that a shotgun with an extremely short barrel is not useful as a traditional bird gun anymore, I can't hit anything with them. So instead of thinking of them as serious hunting guns I consider them as self defense/ survival tools. For that use no choke is not a bad option. If you want to defend yourself at across the room distances, no choke will give you a little spread to increase your chances of a hit. No choke also usually shoots slugs a little better.
While not much use in killing flying birds at 30 or even 20 yards, a short shotgun without a choke could still be a great help in keeping yourself fed in a bad situation. Instead of acting like a gentileman sportsman when you are hungry, you sneak up on your potential food as close as you can. If it flushes within 10 yards, then you have a good chance of bagging it. Better yet you ground sluice your birds. If you are hunting to eat, maybe the best choice would be to quit shooting at flying birds and save your shells for sitting birds or rabbits. You don't need much choke to be a killer rather than a sportsman.