My experience with those screw extractors hasn't been great. With high quality stainless steel bolts found on many bike components the material is a bit too hard for the extractor to 'bite' into them.
They are fine on aluminium alloy bolts and lower grade steel in terms of biting into the bolt and getting enough purchase to unscrew them. You can end up just shearing the bolt cap off.
if you haven't already pre-drilled a nice clean centred hole down the bolt shaft, then it is much more difficult to then get a hole drilled in the end of a broken bolt.
That said, once the bolt cap is gone then the tensile load on the thread will no longer be an issue so the remainder of the bolt shaft usually turns if you can get hold of it.
I'd definitely recommend using that 2mm drill bit first as a fail safe. A bit of light oil on the tip of the drill bit helps too.
You'll be fine Doug. Drilling out titanium bolts on expensive titanium frames is much more nerve wracking.