OK, maybe not the best idea, but you can try to heat up the screw with a small soldering iron.
Let the tip bear a small ball of solder, tip it onto the screw for best thermal transfer.
If the thread weaks up, unscrew carefully.
ATTENTION:
Three mistakes can be made:
1) If the screw is made from brass, iron or any solderable material, the solder may find a way to bond. That means you need a replacement screw!
2) the solder falls apart the tip and ruins some electronic - if you fear that, don't use a solder ball. Try it with the clean tip instead.
3) when you heat up the screw, you´ll also heat the thread into that the screw is fixed. If this thread is made from plastics it could melt...
This method is recommended ONLY for crafters. I guess you will do fine.