In my opinion, any firearm beats a slingshot or a sharp stick in the eye! If a .22 is the only thing manageable for her, that's what I would go for. There are many great choices out there in .22 caliber. It is not clear whether or not she planned on carrying it but my personal favorite is the Ruger Mark III. My wife loves that gun too, and it gives you 10 +1 rounds. It would be a little too large to carry, but certainly very comfortable to shoot even with arthritic hands.