Do you have other snakes or reptiles that could catch mites if your new snake has them? If not, I wouldn't use "PAM" unless your new snake actually has mites, because while it's pretty safe when used as directed, it's never completely risk free. You don't want to use such chemicals unless you actually need them.
Not sure I understand the "risk" of spraying your enclosure in your garage? Safe for your cat, you mean? I'm not sure, honestly. Ask your vet, especially if your cat ever goes in the garage.
Paper towels are great for spotting mites or other problems (such as abnormal stools/urates, mucoid or bloody streaks for example) but not "perfect" for the reasons you asked about. Yes, just minimize ventilation & use a big water bowl for the time being (for more humidity), or offer a humid hide in addition to the other hides (warm & cool). You're right that a complete cage cleaning will disturb the snake to some extent, but they don't "go" that often anyway, so don't worry about it- be as low-key as you can, that's about all you can do.
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