The screws are probably made of 12L14. Hammer, and the other lock screws, are usually made of leaded screw stock. That steel is about one step stronger than cold peanut butter. That is because it is easy to machine and the strength required is very low. You will not find any "hammer screws" made of "better" steel such as 4140. I suggest making your own screws out of whatever you think will work better.
I have never has a single hammer screw break off in a tumbler is half a century. The screw has no stress on it whatsoever.
The hammer is supposed to be so tightly fitted to the tumbler that it takes a fitted square punch to drive it out. To install a tumbler on a hammer required some sort of press. There is a taper fit on the square section. The fit is extremely tight. As previously mentioned, if the hammer is loose on the tumbler, it is not fitted properly, or properly installed.
Tightening the screw is irrelevant to the fit of the two parts. IF a guy had a loose fit and tried to make the hammer tight on the tumbler with the screw I would expect the screw to break.
If a guy were to try to use the screw to seat the hammer on the tumbler using the screw, I'd expect the screw to break.
IF the tumbler to hammer fit was loose I would not be surprised if the screw broke after use and repeated tightenings.
The screw will never break if the hammer is correctly fitted and installed onto the tumbler.
Being a TC gun, realize that they were not perfect. I know some people think they were perfection. Sorry, they were not. They were built in mass and on a budget. Quality was not a high priority. Those guns were made of cast parts. They were not hand fitted or well finished. They were simply thrown together quickly. The main goal was to keep the price down and sell product. I would not be surprised if the hammer and tumbler were not fitted properly as originally made. Perhaps make a new tumbler that actually fits the hammer. That is what I'd do. Being a metallurgist that should be no problem.