Dont use swarfega. I was once accosted by my fellow employees and cable tied to a parts trolley. The receptionist then proceeded to coat my genital area in axle grease and strip me naked. I was then hosed with a fire hose for a bit more fun. This wasnt normal practice i was about to be married btw.
Anyhow i went in the company showers armed with a tub of swarfega and it was terrible. It just turned my genital area into a big mush of grease and soap which got ever more clarty. I was red raw and getting desperate
I then got a bottle of washing up liquid and by magic it dissapeared.
For a cat i would just wash it in the liquid and then dump it in the bath to rinse.
If you are scared of the consequences then why not put it in a plastic pet box and then dump it in the bath at a suffcient depth. you could even dunk it a few times just for fun 😉 personally i have placed a cat in the shower before (As punishment for digging up carpets) and i did end with some rather nice cuts to my arms, but nothing to bad