J.N.
Go to a regular cup, and have him drink at the table. There is absolutely no reason that a child needs to carry a cup around - especially if there is anything other than water in it. Serve a drink while he is at the table or in the high chair, have him finish it, and then he can go off to play. Get him in that habit now and you won't have nearly as many issues later.
Once my kids were 2, I also got them sports bottles, where they can close and open the lid. But it's for water only.