I have a styptic pencil I use once in a while for shaving cuts. It's the kind you can buy at drugstores.

Would it also be safe to use on a cat's nail if I accidentally cut into the quick while trimming, or do cats require a special kind of styptic pencil/powder?

all syptic does the same thing, clots the blood to help stop it and it's also a medicine to stop infection. if you don't have syptic powder, you can also use baking powder, (its the same consistency and acts as a syptic).. but try to avoid cutting the cats nails too short, they don't tolerate it like dogs do, and after you cut them, you will never be able to do their nails again..