With screw extractors you do need to be careful, they are a hardened steel and can be brittle. They're ideal when extracting the screw from blind hole if particularly the screw hasn't reached the bottom of the hole, if the head has sheared off the bolt then sometimes the load on the thread is released making it an easy process, if the screw stub is tight onto the bottom then there is more friction holding it in and the load remains on the thread. Personally i would try this first, but then I have them to hand, and have used them before with a greater degree of success than failure.
If you try to drill out the bolt you will more than llikely be off centre and catch a side of the thread, both this method and screw extractors require an amount of patience.
You could over drill the hole and helicoil back to the original size.