My first grey, Eve, was like Klute. It wasn't so much the nail clipping, it was holding the leg. She'd let out the Greyhound Scream of Death (GSOD) anytime someone -- even the vet -- even thought about holding her feet, and buck and jerk like a bronco. Like Klute, she was refused by professional groomers.
After months of sweet talk, desensitation attempts, bribes, getting one or two nails at a time clipped, I was desperate. I used a controversial method -- the neck scruff. I gently but authoritatively grabbed the loose skin at the back of her neck with one hand, and moved it LEFT RIGHT one time each. This is how mother dogs sometimes discipline their puppies. I said in a firm voice, "Nail clipping is necessary for your safety. You WILL let me do it." And she did. I almost fell over from shock. She never liked nail clipping, but she put up with it. I think I only had to re-scruff once over the next 7 years.
This post is probably going to get some flak from people who like to use only positive training methods, but as I said, I was desperate. Eve was a confident girl who didn't have a nervous bone in her body. A neck scruff wasn't going to traumatize her. She did make sure that she got her required treat after every foot trimmed.
I've never used the neck scruff on any of my other greys -- the traditional desensitization methods (sweet talk, touching feet gently, treats) worked just fine on all of them except one. He had pemphigus -- an autoimmune disease characterized by abnormally growing, painful nails. You can imagine what nail trimming was like. Early on I was giving him a bath in the tub, and he became very docile. Sure enough, he let me clip his nails in the tub. I did always put on his muzzle, just in case.