There's a simple solution: Cut your cat's nails.
It's easy, and with a little patience, most cats can learn to tolerate it. Mine do.
Every other week, all of my cats enter the beauty salon (also known as the bathroom) and have their nails cut. I gently pinch each toe with the fingers of my left hand and trim the nails with standard nail clippers in my right hand.
I just snip off the tips, carefully avoiding the pink blood vessels near the base of the nail. With regular clipping, that blood-filled core moves down the nail, closer to the paw, so I can cut back more nail during these sessions.
While my cats do not like to have their nails cut, they are accustomed to these cutting sessions and they don't protest. I don't scruff them, restrain them or wrap them in towels. I just hold them on my lap and snip away. This is likely because I've been cutting their nails since they were kittens, and they know I will not hurt them.
This page from WSU has wonderful illustrations on this topic, if you'd like more information.