Taking apart old G.E.C. Hair Dryer? Asbestos?

Easiest thing would be to just pick another appliance for the "recycled product" project. If you need to use this specific appliance, take it outside where there is plenty of ventilation and carefully open it up trying to not stirr up any dust. Usually, if asbestos is there, it will be in the form of whitish paper or cardboard-like material between the heating element and surrounding material/parts. Sometimes you find a sheet of mica or a material that looks like mica flakes bonded to gether with high-temp adhesive, this is not asbestos. I don't think there is any reason for panic, most of the people who had problems with asbestos were working in industries where they were exposed to it every day for years.