You can get a new screw from most Ace Hardware stores. Many of them have a gun screw collection in the little drawer boxes sets. Most of them are long, but have correct threads and a variety of heads. Uses calipers and a grinder/file to adjust length. Slightly round the tip portion after grinding.

I have a lot of taps. With small screws I usually tap a hole in piece of brass and use it to hold the screw while working on it.