In the first example, it sounds as if they are diagnosing medical complaints of the hand. In that case, I think that "hand profile" means an evaluation of how you use your hand on a regular basis. If you work on a computer and type steadily for eight hours per day, you are prone to carpal-tunnel syndrome. Other people, like cashiers and construction workers, are liable to suffer from repetitive stress injuries to their hands and wrists.
In the Disney example, they are talking about a method of identifying people - you place the palm of your hand on a machine and it will confirm whether or not you are the rightful owner of the pass you are using.