Honestly it's a good thing your cat is being cautious rather than expressing immediate interest, which I would be way more concerned about.
I also keep my snakes in different rooms away from my cats. One of my cats has zero interest in my snakes but I still would never trust him around my snakes, since cats my nature are curious and unpredictable. My youngest one I especially don't trust lol.
And when they do decide to be unpredictable, they are FAST. You will have no chance to stop an accident happening if a cat decides to tap into predator mode.
I once had my youngest outside on the front porch with me with her harness and leash (yes I walk my cats lol). We usually sit by the steps together. There are shrubs beside the porch and suddenly I see my cat staring into the bush, thinking oh she sees a bug. The usual.
Suddenly she lunges forward and rears back with a little bird in her mouth. Not even three seconds and the bird is unquestionably, completely DEAD before I could even register what was happening.
Keep in mind this all happened right in front of me with her on a harness AND leash. She was just too fast for me to react. I didn't even know there was a bird in there!
Anyways your cat will eventually adapt and either not care, or become more bold and curious. So I really don't think the blanket is necessary and I doubt she's as stressed as you think she is, especially if she's going in the room on her own accord.
Either way I wouldn't worry about kitty. She'll be fine
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