I wouldn’t bathe her yet. She will still be decompressing and needs as little stress as possible. If she’s shaking and that anxious about it, she’s really not ready.
If you can leave it till the warmer weather, I would do something along the lines of Polly’s advice, maybe outside and yes, a shallow paddling pool would work - they do them for dogs that fold away after use and won’t be damaged by their claws. We bought a massive plastic plantpot, designed for planting trees for our large breed dogs and used the hose attached to a mixer tap, so we had warm water and it worked a treat.
Use the time between now and the warmer weather to introduce the process Polly suggested and work up to her accepting actually being washed.
We have used the no-rinse foam on one of ours in the past, when they couldn’t be bathed, but desperately needed it. Just google no-rinse dog shampoo, there are loads on the market, including ones with natural ingredients, some are sprays, some foams and some like dry shampoo - I have only used the foam on a dog with a thick coat, but it did the trick.
I am not big on regular dog bathing though, especially with outdoor breeds like the Mioritic. Their coats are essentially climate control and will be pretty weatherproof, washing will adversely affect that.