Busterswoodshop,
If you fit 22 Mags in the cylinder as you said, there's nothing to double check, it's a 22 mag. It was not designed to shoot any other .22s, however it's not unsafe, but it's a waste of ammo because accuracy will be less than mediocre. You may even get split cases on occasion but .22 cases are throw away anyhow.
After scrubbing your cylinder face clean, look at it in sunlight you should see the last 3 numbers of the gun's serial # engraved on the front. That will confirm two things: it was an original cylinder for your gun and your gun is a convertible with a missing 22 LR cylinder. Convertible guns were not stamped as such, they are only marked .22 like yours.
You can find 22 LR cylinders by posting a want ad on this forum for $75 to $100. Measure the overall length of yours and get one at least that long or longer. You can slightly trim (stone) the cylinder pin hub on the front of it to fit your frame. But you can't make a short one longer.
Once you get a 22 LR cylinder, it is designed to shoot any of the .22 CB, short, long or LR ammo. The problem is most of those are more expensive than LRs and have less performance. However I do shoot .22 CBs and subsonic longs because they are so quiet. They are great for pests or plinking when noise or the lack of ear muffs is a consideration.
While many single sixes used to be for sale without their 22 mag cylinders because most were not used and stored away when the gun was sold, there seems to be a new trend. More and more old model 3 screw guns are being purchased with one cylinder and to the chagrin of the buyer, they find out later that it's the 22 mag. Both old model cylinders are fluted and at a glance can be mistaken for each other.
It appears that less ethical sellers hold back the 22 LR cylinder, and sell the 22 mag cylinder, which usually looks like new, in the gun so they get about the same price for the gun or more with only one cylinder cause the gun looks in better shape. Then they sell the 22 LR cylinder for another $100 because they are harder to find than mag cylinders and sell for more!