My cat recognises several words thanks to consistent usage: "Clawsewitz", which is her name; "dinner", which means yummy wet food is incoming; "hot", which means keep off the hob; "come", which means saunter over here if you feel like it; and so on. But there is one word I deliberately taught her that is more important than every one of the previous, and that's "finished".
It means "I've stopped doing mean things to you. You can relax."
Teaching this word or phrase is simple enough if you're logical and consistent. Whenever I clip my cat's claws, or run the hoover, or do any other necessary but offensive tasks, the last thing I do is say "finished!" and immediately behave normally towards her. No apologies; don't follow your cat in distress if it goes off to sulk; just be your usual self, whether in your case that means benignly ignoring the cat, giving it a pat on the way past or smiling and talking to it. Your cat picks up cues from your body language almost as well as a dog does, and the message you want to convey is "what? Oh, that's over and done with. I've forgotten about it already*."
(Sometimes I give her a treat at the same time as "finished", which works if your cat's food-motivated, but do not use it as a bribe to get your cat to come back if it runs away. Just toss it in the cat's direction and be unconcerned. If the cat needs to get some distance after a procedure, then that's what the cat needs. You're creating a feeling of safety and chasing the cat will undo that.)
Terminology? I use "finished", but you could use "all done" or "it's over" or anything you like, as long as you use the same words each time and it's audibly distinct from your other commands (cats have great hearing but in my experience they're not as wired to listen to words as dogs are).
Why do I say this is the most important word you can teach? Well, cats do not understand "horrible but necessary". The concept that anything might happen that is not concordant with the cat's wishes is pretty much unthinkable to a cat, and being captured and put through indignities is pretty confusing, even if there's no significant discomfort involved. Even after the bathtime or flea-combing or dew-claw molestation or carpet-hoovering is over, the cat will be upset and uncertain that it can trust you again. After all, there was no warning before you suddenly turned evil. You could do it again at any time! You are the enemy, and an arbitrary, capricious one at that, and you must be evaded!
This is why you need a clear disconnect. Your "finished" command, backed up with appropriate body language, signals a definite end to the stressful horrible things and a return to business as usual. This is a lot less upsetting for the cat than ending the encounter on a guilty, overcompensatory note ("my human is upset; now I know I should feel awful about this process") – or, even worse, on an angry note when the yowling devil claws its way out of your arms.
You must, of course, be truthful. No chasing after the cat. No turning the hoover back on to get a spot you missed.
Your cat may never enjoy procedures like claw-clipping, but that's not the goal of the "finished" command. Of the cats I've known, all of them have quite reasonably hated the clippers and most made an almighty fuss at some point in the process. Teaching "finished" doesn't help much with that (if there's interest I could write a future post with a few tips that will). The ending, though, changed completely. Our former cat Piper gradually wound down his post-pedi pique procedure from running out of the house, to leaving the room, to jumping down from the counter, to taking a token step away and then returning to his usual begging for food.
Take a step into your cat's mind and you'll find that, never mind the 'aloof' image commonly ascribed to felinity**, your cat needs things to be logical and make sense. Cats can and will adapt to all manner of stupid things their humans do, just as long as they know what's what. "Finished" means safety, and that's why it's the most important word you can teach.
Note to people with proper pets: There's no reason the above advice can't be applied to dogs too.
* Cats instinctively understand pretending things never happened. They do it all the time, right after they embarrass themselves.
** Which makes no more sense than their reputation for being graceful, unless you actually believe the cat's "I meant to do that" face after it slides sideways off the counter and takes a towel and half the drying-up with it. Everyone used to think different human cultures from theirs were inscrutable; then we got to know them and found they weren't, they just did slightly different things with tea.
Edit: My mum points out that she was the one who taught me this, from my earliest days growing up with Golden Retriever puppies. I barely remember anything from that young, but looks like I was brung up right…