My experience with drilling SS allen head bolts. My oil pan bolts are SS socket heads. I had the best results starting the holes with a HSS bit, then finish with a cobalt. Since the hole is being started on a round surface the narrow 1/16 bit tends to walk. The HSS bit will tend to cut with a lighter pressure than a cobalt, reducing the incidence of walking. Once the hole is started (dimple) I would finish the hole with a cobalt, when you good pressure can be applied and the cobalt cuts better and lasts longer. FWIW, my experience.
Joe
For small round pieces, grind a bit of a flat spot opposite a wrenching flat with a small stone in a Dremmel or similar. Drill through the flat spot.
Keep your small broken bits in a jar. Sharpen them all some day. Use a short bit choked up in the drill press chuck and it won't wander around. If you clamp the vise to the table and complete one screw or bolt, adjust the vice location to get a perfect hole and tighten the clamps. All subsequent holes will be identical.
Debur the holes by hand with the screws vice gripped in a piece of plastic, and the drill bit in a slow turning battery drill motor. The bit needs to be three times the hole diameter. Shallow angle flutes. You can manufacture dozens of wire holes in short order. The flat spot will vanish when the chamfer is generated.
Wear a thick welding glove on the vice grip hand and wear safety glasses.
Real safety glasses are at least 3 MM thick at the thinnest point, and are heat treated so as to fail as little squares. Have your glasses checked. Most are less than 1MM in places. Some never get heat treated. Hardened glass with scratches becomes a bomb that can fail at the most unfortunate time. (Murphy).
A real safety glass lens must survive a one inch diameter steel ball dropped from 80 inches. Buy real safety glasses with a well known brand name. Bausch and Lomb or American Optical. Discard glasses with scratched lenses.
Lynn E. Hanover