Carl,
Can you find or make a screw with the correct thread? If not, the best idea is to repair the old one. The countersink is damaged ant it might be easier to clean it up and match the larger diameter of the countersink with repairing the head of the screw. It is easier to work on the outside of anything than the inside. You would be wise to follow Kutter's advice when repairing and "clocking" the screw head. The finished screw head will likely want matching engraving.
I have absolutely no experience with laser welding, but it may offer some advantages to repairing the screw head. I don't mean to criticize anyone else's advice, but my own former experience indicates it would be very likely that I would create new damage by "run outs" trying to reach the end of a screw slot with a motor tool. Other people may have better control.
Mike