What could Richard III have done differently?

1483: Edward IV dies. Power struggle ensues, we all know what happens next. Let's say Richard didn't usurp the throne. He didn't move quickly to get rid of the Woodvilles and others he deemed a threat. He just accepted he was Lord protector, did his duty, looked after the prices, and saw to their coronation. What would have happened? Was there really any threat to him that meant he had to act the way he did, or, had he just done what was asked of him in Edward ivs will, seen to it that the edward v was secured to his throne, would he have been safe? Able to just carry on his duties as usual, or would the Woodvilles or some other faction have still tried to get rid of him?