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Cellophane wrapping on deck can be shrink with an hair dryer if cellophane wrinkles due humidity.

Is there any danger of damaging the deck / melting glue / sticking the cellophane to the tuck?

Do you have pictures to demonstrate?

I've done it myself plenty of times. I actually do it with a heat gun; much hotter than a hair dryer but it's faster. Decks don't suffer anything if you do it carefully. Avoid getting too close and stressing the cellophane with the heat, because it may break. If anything bad is happening, the cello is the first to tell you.

Try on some cheap ones to get the hang of it but it's not a big deal.

As Dan noted, try a few inexpensive decks before you go whipping on your precious decks, and it is pretty easy to get it right. Just don't expect to use a blow torch.