Your cattleya is just doing what it was evolved to do - those aerial roots are actually trying to access the humidity and moisture in the air, mimicking how these orchids grow on trees in tropical forests. The fact that they're white and healthy-looking is a great sign. You don't need to do anything special with them, but here's the thing most guides skip: if they're bothering you aesthetically, you can gently guide them back into the pot or alongside it using a soft tie or stake, rather than removing them entirely. They'll keep trying to reach outward though, so it's more of a cosmetic redirect than a permanent solution.
What's actually useful is paying attention to what triggered this growth. Aerial roots usually develop when orchids want more humidity or air circulation than the potting medium is providing. If you live somewhere dry, your cattleya might be telling you it'd appreciate occasional misting or a spot with better air movement. You could also try repotting into slightly larger media (bark chips tend to dry faster than sphagnum) if you're watering frequently. The roots themselves are harmless - they're a feature, not a bug.