Shiryu defeating Mihawk would hype him up as an absolutely crazy bloodlusted monster worthy of being the RHM of the strongest character ever in prime Teach. Yes, he's way too weak to do that, at least right now. And it probably won't happen.
But I really liked the idea. His (and his captain's) dread factor would skyrocket so fucking much. He'd become one of the worst nightmares of One Piece ever.