DH and I took meclazine (Bonine) every single day of our cruise last summer. It did not make us drowsy, AND we were able to drink while taking it.
Our sons are joining us on our cruise this summer (in 2 weeks!), and our pediatrician said it was perfectly fine for DSs to take meclazine while on the cruise. Our DSs are 16 and 13, though. Just to be sure, I'd give your pediatrician a call, Greg!!
P.S. You should start taking the Bonine the day BEFORE you sail, and then continue taking it each morning, during the cruise because it's much better, and easier, to prevent seasickness than to try and treat it once it hits you. Take it even on the days you are in a port. The idea is to keep a steady flow of the medication in your system.