Help! Looking for a cool toned brown felt tip eyeliner pen

I have downturned eyes and cool toned, fair skin. I’m looking for a felt tip eyeliner pen specifically because I love a small sharp wing.

I know eyeshadow and a brush is an option, but with my lid shape it’s hard to make it look clean.

I currently use the nyx epic ink liner in milk chocolate, but it feels like a very warm brown on me. I appreciate all suggestions for cool toned skin!!! Thanks!