There already is an option. During the three times you are asked to save the game (consider them as checkpoints), there will be a button at the bottom of the screen that says Skip Current Bout. That will allow you to skip through the scenes.
However, the court scenes after the third checkpoint involve the Main 6 (Leo, Jin, Joseph, Ridge, Koku and Runan). I recommend not skipping through that part, since dialogue vastly differs between the six dateables.