Not trying to restate the obvious, but the shutter speed used caused frames captured with blurred motion, and that resulting smear is leaving areas of gray surrounding the quickly moving objects:
this makes it difficult/impossible to use the keyers to get a good looking key, as these areas are a graduation of luminance, and color.
My suggestion would be to have an electronic graphics person rotoscope a matte that trims the key to the shape of the hand, most likely using After Effects. This will probably need to be done frame by frame. They will also need to manipulate the color and luminance of the fill video so that the partial transparency that reveals the white bg is darkened and colored to skin tones to help hide the repair.
Ambitious, time consuming, and expensive. You should probably have a short clip (30-40 frames) rotoscoped to see if you are happy enough with the result to commit to the process.
MtD