Here's my trick: Use tweezers. Do the initial separation using the razor on one corner and once you have the corner up grab it with a set of tweezers. This allows you to get behind the screen without having to bend the ribbon cable nearly as much, which reduces the chance of breaking it by bending it back and forth.
Even better- once you have the corner up far enough, use the tweezers..I guess you'd say...sideways. The idea would be to end up rolling the film around the tweezers in a cylindrical shape. Do this slowly but firmly and youll find the adhesive usually comes off rather cleanly and easily, and you'll only rarely have to scrape any off.
