The way I understand it, if in a combat round he decided to use Dragon Style, he would use it both for grappling and for Strikes/Sweeps. However, he could certainly decide to switch and NOT to use Dragon style for a particular combat round, but then he wouldn't of course get the +5 to init either. I wouldn't allow mixing two styles during a single round, though.
Of course, if you want to confuse your opponent, switching styles between rounds might be a good idea. In fact, I would probably allow some minor advantage for doing that if your opponent couldn't keep up with you (through a combat perception roll, or something such). This would give an edge to people who are highly proficient (read: fully trained for their level = 3+3xLvl ranks) in several different fighting styles.