Problem solved.
I just got back from taking the catz to get their weapons of mass destruction trimmed, and they are now not speaking to me.
They’re sulking on my bed.
Ah! We trimmed our catz earlier this week. Shannon sat on my lap telling me how offended she was, but Wednesday had to be restrained with gloves and a towel over her head.
My kitty just lays quietly in my lap and lets me nick her pointies off with ordinary nail clippers. I only take off about the last 1/8 of an inch, so I never even come close to the quick, and I hold the clippers perpendicular to the sides of the claw so that they won’t squeeze the sides of the claw together as the cut is made.
Her royal catness isn’t over the moon about the process, but I can do it in less than five minutes every two to three months, I don’t have to leave the house, she doesn’t have to ride in the four-wheeled traumatizer, and it costs nothing.