Like the others, I offer both condolences and a warm welcome to the forum.
Your gun probably dates from 1956. One of your photos shows that it uses an assembly process not involving an upper side plate screw; that screw was done away with in a 1955 engineering change. Also, I bet the 275xxx number IS the serial number, and the K will be found separated from it. If so, that is further evidence for 1956. A lot of K27xxxx guns shipped in that year. And as previously noted, the shape of the hammer indicates postwar manufacture before 1957.
Look at the back of the cylinder. You should see an isolated K between two charge holes, and then the 275xxx number just after the second hole. You should also see that number (with its preceding K) on the flat underside of the barrel when the cylinder is open, It will also be seen on the steel butt of the gun when the target stocks are removed.
The target stocks on your gun are not original, as someone pointed out. These are a later style with a speedloader cutout. But the gun previously had the earlier type of target stocks on it. You can deduce that from the curving grime lines above the right stock panel and on the left where the speedloader cutout is seen. You might look around the house to see if those older stocks are still there. They have some value in their own right.
The S&W K-frame .22s are regarded by many as the finest .22 revolvers ever made. You have inherited a classic that will be perfect for everything from target shooting to plinking to snake protection on field trips, if you live in a part of the world where field trips are possible. There are lots of K-22 fanciers on this forum (I am one) and some of us have more than one we like them so much.
An early word on ammunition. Not every brand of ammunition functions equally well in K-22 revolvers. Try several types, and just stop using the ones where the cases tend to stick in the cylinder and give you ejector problems.
