A friend who's a veterinary technician certified in Fear Free techniques once told me about a way to help trim uncooperative dogs' nails, but I haven't tried it. It involves using a mesh screen with boxes large enough that the dog's nails fit through. The dog stands on the mesh and the person trims the nails from below. This avoids having to hold or restrain the paw which is often the thing the dog doesn't like, as mentioned above. I imagine a Dremel would work well with this if the dog will tolerate it, but regular clippers might work as well.
My rescue border terrier X was initially very bitey about having his feet handled, but since he's only 18 pounds I used a soft muzzle and just dremeled him on my lap. He was perfectly quiet with the muzzle. I eventually stopped using it and he's still fine with nail care. OTOH, one of our Border Collies will not allow me to do her nails, but since she'd happily walk through fire for my husband, I just have him hold her leash and I quickly clip her nails without incident.
Good luck with Katie!
Amy