Reddit reviews C&C Metal Products 5051 Flat Florentine Metal Button, Size 30 Ligne, Antique Nickel, 36-Pack

I can imagine finding travel samples of makeup and supergluing this type of button to the top of the cap or these things to the side of the cap, then threading a paper clip through the hole. You could then attach the paper clip directly to your key ring.

Or you could superglue a thick hair elastic to the cap and put a key ring through it. Even a strip of fabric tied in a ring and glued to the cap would work.

There are tons of tiny jars and things to make your makeup portable, so making them key-ring friendly shouldn't be too difficult. However, I would test cap strength first-- My key ring is tossed in my pocket, thrown on the desk, pulled out of a tangle of other pocket stuff, and generally moves around a lot, whatever I attach to it goes through the same rough treatment.