^^ good luck with using extractors on stainless. The drilling alone is techy. Drill press n cooling fluid needed etc. Waste of time trying if you haven't done that stuff before.
Thats why i asked if it is stuck as there are different methods to unstick it first. If its not stuck and isnt a clean break, it may rotate as per the other post above.
A handyman trying a hand drill and a 3 or 4mm bit will almost certainly wander off centre and fk the fuse.
In my experience drilling and extracting the screw out as a "home machinist" is highly dependent on what the broken piece of screw looks like. If it's shaped in a way that allows you to start that drill bit in the middle easily (flat on top or some kind of depression in the middle) your good but it's probably sheared off at an angle and it's going to be hard to get the bit to go straight and centered. This is the part a drill press is good for.
maybe play with something like this to see if the carbon part on the outside can serve as a drill guide on the smooth flange around the drill side do the extractor.