If you are going to paint it, my advice is to use 2k epoxy based spray-paint instead standard acrylic spray-paint.
Acrylic paint, on surfaces that get touched/handled a lot, can get sticky/icky just like the rubber coating.
The triglycerides and fatty acids in your sebum (oils/grease your skin produces) soften the acrylic.
This is a common problem with painted doors, furniture, windows, etc.
Epoxy based paint does not have this problem.