Usually removing standard sized snapped screws is a difficult job, but in this instance since we're using seriously tiny screws it makes the job.... much, much harder to resolve.
Drilling out is difficult and could cause more problems. ie. damaging threads.
But since you oiled the screw prior to fit, removal should be slightly easier.
I propose to get a small hammer and a very small flat screwdriver with a hardened tip, or even better just a hardened pointed tool. The object here is to try and etch in a deep mark (make an indent) in one side of the snapped screw head (near the edge). Once a mark is made in the screw head, use the tool and the hammer to tap the damaged screw in a counterclockwise direction. Hopefully this will loosen the screw enough that it will just unwind and pop out with no damage to internal threads. Hope that makes some sense.
If the indent you make is deep enough for the tool to bite and right on the edge of the damaged screw, you should be able to make some progress. Mark the screw edge and the chassis with a permanent marker so you can see any small movement as you tap away. π Good luck.