I have drilled out many a tap.especially small ones,with a carbide drill. Run it at about 4000 rpm with NO coolant or oil. The way it works is the carbide gets the hardened steel,or HSS very hot. This removes the temper and the drill scoops it out as it is de tempered.
Exactly what I have used are straight flute carbide drills,or spade tip carbide drills(even better as they don't break as easily). Some years ago,I found a guy selling assortments of 10 small solid carbide end mills,TIN coated nice and gold. They are assorted sizes,and were $10.00 per pack. I wish I'd bought more,as the guy has disappeared. Might have died. These little end mills can drill out broken taps beautifully and I never have broken one.
I haven't been able to find a source for the little 10 packs,but I have seen single ones for sale on Ebay. You might Google around to find them. They have 1/8" shanks,and range from about 1/16" to 1/8",with lots of in between sizes. Exactly what size they are I can't say. They might be metric. I just select the size I need for drilling out the tap. I run them at the top speed in my Bridgeport type mill.