Gunsmithing: how to remove rusted screws from riflescope rings?

I don't you will find an extractor small enough. Drilling the screws out with a bit the correct size to us a tap for that size screw would be best. Drill it out (carefully don't get into the metal outside the screw) and then tap it. Unless the rings are the original that came on the rifle, I would just drill the screw heads off, salvage the scope and replace the rings.