I'm not entirely clear what you are asking, but it seems you are not considering that a GIF only can have a single transparent color. Thus unless you prepare your image accordingly there will always be fringes from antialaising. that's just how it is. No magic solutions here. You realyl have to work on your source material to make it GIF-friendly.
When you create the image of the hand, are you creating it as a transparent layer rather than white? Create your image on a transparent layer and there will be no white in the image. If you know the color of your background, you can also use that background color on your layer with your image to create an animated gif. See the example below: