If at all possible, it would be MUCH better to find a way to remove the damaged screw and NOT damage the flange it is through. As posted above, solder will NOT give the mechanical strength needed to hold down the heatsink at that attachment point. And having three attachments out of four may not do the job, either.
How to remove the screw? The technique depends a lot on what design of screw, and on how damaged it is. IF the screw head is exposed ABOVE the flange but simply is damaged in the middle where you fit in the screwdriver, you can try a different tool. My favourite for this is small locking pliers, aka Vise-Grip. You can use this to grip the screw head from its sides very tightly, and then rotate it. Even a small rotation to start may break it free enough that you can turn it out the rest of the way with a badly-fitting screwdriver or your fingers, or even tweezers. If not, you can loosen the pliers, re-position them, and turn a bit more until it comes really loose.
If the screw head is not reachable (recessed, maybe?) there's a different way. But like your cutting plan, this generates metal fragments that can scatter, so you really need to clean up after. AND you need some special tools: a small drill bit, and a small version of a tool called an "easy-out". You drill a small hole down into the screw head part way. The easy-out has a narrow cone-shaped tip with spiral grooves around it. You place its tip into the hole and then turn it backwards as if you were UN screwing the screw. The spiral threads are made so they bite into the sides of the hole you drilled and turn the screw out.
Last option. Again, drilling a hole in the screw head, etc. But this time you use a drill bit wide enough that it will basically drill out the entire diameter of the threaded screw shaft under the head. BUT you REALLY need to NOT drill down too far - only far enough to disconnect the head from the screw shaft underneath. Then you can get the heatsink off the CPU. The remainder of the screw shaft should then be exposed with a stub sticking up out of the hole underneath. THAT you can grab with pliers - maybe the small Vise-Grip type if you have it - and turn it out.