This will cause the nail to extend making it easier to cut. If it is a clear colored nail, you should be able to see a faint pink line through the side of the nail. If you trim the nail too short and cut through the pink line, she will bleed. Because we just want to blunt her nails to prevent damage from her clawing, you just need to cut the sharp tip off. This should not cause any bleeding.
Most pet stores carry nail clippers designed for cats.
Nail caps can also be tried . Nail caps are small rubber nail covers that are glued directly over a trimmed toe nail. Once on, they typically last 4-6 weeks before new caps need to be applied. I would try all of the above methods before moving on to surgery. If all else fails, then declawing would be your next step.