cats have this place at the back of their neck...
where if you really grab the skin / fat / whatever really quite firmly...
it paralyses them.

mummy cat grabs her kittens there so she can carry them without them struggling and squirming.

if you manage to get a good grip of her there and don't let go of that through the process then that should make things a whole heap easier.

can you enlist someone to help you?

that way... one person could grip her while the other person could wash her...

alternatively... you don't happen to have three hands - do you?

;-)