It's surprising how much bad advise you've received on this thread. It's seems many paid no attention to your original post, and just suggested their own favorite .22 LR revolver.

Major requirements: light weight, light recoil. Weight first. You must buy an alloy frame gun. This eliminates all steel frame guns. Further more, it would eliminate K and L-frames, with regard to rimfires.

Which brings us to cartridge selection. Obviously, the .22 Long Rifle is the only viable choice. The .22 Mag is extremely loud and harsh to shoot in a snub nose revolver. Plus, it's more expensive and has a smaller selection of ammo compared to the Long Rifle. The round excels in rifles. In revolvers, it's alleged advantages are unrealized due to short barrels and cylinder gaps.

Okay. By logic and elimination we're at an alloy J-frame .22 LR. S&W gives you two to choose from.:

The Model 317 Kit Gun (SKU: 160221). A very good option. 8-shots. Exposed hammer makes it a little "snaggy". But I like the ability to shoot both single action and double. Has a lock, which is good for grand kids.

The Model 43 C (SKU: 103043). Another good option. This gun has a Centennial shape, so there is no exposed hammer. Double action only. Also a 8-shot J-frame. Probably the best choice, for strictly self defense. So light it almost floats. Recoil nonexistent.

Both are known for relatively heavy trigger pulls. This gets a lot better the more the gun is shot. Get some .22 snap caps, or dry wall anchors. Over time, cycled the action 1,000 times. You don't have to do it all on the first night, it can be done over weeks. You'll be pleased with how much smoother and lighter it feels.

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~ S&W aficionado in training ~