22lr is still readily available and if you train with it, I think something like a Smith & Wesson 43c is a viable pocket carry gun. It won't blow somebody's head off but it's loud and painful if not lethal when shot at close range. Which is what you want from a small CCW... basically time to get away and put distance between yourself and the threat. Besides in today's climate blowing a 45 through some vibrant personage might get you a long term vacation alongside insurec... patriots.
Realistically I'm not going to carry a 45 24-7-365 but I can carry an 11oz J-frame with 8-shots without any burden.
I can't imagine any scenario using an air gun for self-defense that doesn't seem to be a last ditch effort. If you're far enough away to shoot at distance you're probably better off increasing distance rather than pissing the bad guy off or revealing your position. If they are close enough to be an imminent threat then a baseball bat is a heck of a lot more reliable with quick follow up.
Avoidance is going to be very important to any defense. Showing that you're not a murderous gun nut but simply a responsible citizen looking to avoid violent confrontations is going to be how you avoid the bogus charges these awful prosecutors are going to try to hang on anyone who defends themself.

This is such good advice it is worth quoting here again. I've got a Buckmark with a 4" barrel to carry and am looking for a smaller platform. I keep a 10/22 in a closet with a 25 round magazine and a spare beside it... my Mossy 500 is by the bed. My airguns are to make food and a good spring rifle in the 14 to 20 foot pound range will do that 24 x 7 x 365, quietly and efficiently out to "far enough" yards.
Yes.