I have used these Bullet drills for years, with a slow speed and cutting oil Stainless is no problem. And due to their shape they actually cut a washer out of the material so you have a perfect hole with no burr on either side, and they will not grab suddenly and pull through. Various companies make drills with this tip profile.
https://www.powertoolsdirect.com/black-and-decker-piranha-bullet-drill-bit-range
