Yeah, I'd definitely say use lukewarm water, and gently comb it out, let it dry and style it from there. If the first time doesn't work, you can do that a couple times, with spritzing water, combing it, drying it, and then it should be good to go!
As for preventing the cat from getting to it, maybe look into getting a heavy storage box. A tote, zip up travel luggage, or a hope chest of some kind would be best. Something the cat can't lift, unzip, or unhinge. You can find REALLY cheap options at thrift shops. Like I know in the west, and east coast US I've been able to find those things for under $10 at Goodwill.
Best of luck living with a cat that seems to have radical opinions on long hair!