This has worked for me in the past:
If you can get a punch into or onto the screw and give it a couple good raps with a hammer , it will help break the bond, or take a 1/4" screw driver bit of the screw size, put it in hole give a couple shots.
I have stripped torq head screws and pounded a robertson or hex into the hole and turned them out easily after the hammering.
I wouldn't go to the smith just yet.