Back up cup similar to MCUK

I'm looking to get another cup to use as well as having my mooncup UK. I want to be able to keep the other cup in my bag in case of emergency (I'm on a mini-pill and have irregular periods so I can't put my cup in when I think I'm due). I'm looking for something which is similar in size to the small MCUK but made out of something which doesn't pick up fluff and lint so easily.

Even when I keep my cup inside it's little bag inside the pocket of my bag it ends up covered in fluff! I doubt that my bag fluff is very harmful but I don't like the thought of it ending up inside my vagina really. And it's not always convenient to rinse the cup in public loos.

If anyone can recommend a less sticky cup then it would be greatly appreciated! Thanks!