I took the plunge! Combined all the advice, and got in the glass-doored shower fully clothed with the cat. She was sceptical, but ok. I put her in the corned while the water warmed up, and then sprayed, shampooed and rinsed that little sucker off. No protests from kitty until the final rinsing when the just lost it and howled pathetically. I turned the water off, and got the first of 3 towels. She let me dry her properly, seemed just as fond of me as before (just barely), and huffed of to sit in front of the aquarium and lick herself.
She did not seem to mind all that much until the end, and though I usually despise reading too much into animal behavior I did get the feeling she understood I was helping her, not trying to torture her. Not a scratch on me, this went swell!