Think of it this way: trimming their nails makes them panic momentarily and you feel bad for a few minutes, but they feel better and are so much more comfortable when it's all done. And: They will get used to it if you make it a regular routine.
Not trimming will mean you won't have to deal with those few moments where you feel you're torturing them but can and very likely will cause injuries, pain, infection, stress, and potentially high vet bills for you.
Logically you know it isn't hurting them, so if you can get over feeling that you are, you're on your way. Once they realize you aren't going to cause them discomfort or pain, they settle for it and tolerate it for future clippings.
I use a regular (human) toenail clipper and as many others have noted, a treat (bribing them) helps tremendously. Try giving them a very special treat that is reserved only for nail trimmings. I use kiwi fruit or a banana, which they just *love* and get only when we do some "horrible" grooming routine. Once they can associate a beloved treat with some momentary discomfort, at least in my case, they are much more tolerable of the whole fiasco.
Good luck to you.