I really like the sound of Warrick. And while I know Warwick is the original spelling, a bearer in the U.S. might have trouble getting his name pronounced correctly. Since the towns / neighborhoods of Warwick and Chiswick (pronounced war-ik and chiz-ik, respectively) are in the U.K. and not here in the states, everyone would probably read Warwick as war-WIK, and Warrick as war-ik.So that's why, while Warwick admittedly looks better, I would use the spelling Warrick.
So that's why, while Warwick admittedly looks better, I would use the spelling Warrick.