it would probably not be best to actually put water into the box, the water bottle could leak and you wouldnt want the box getting soggy and breaking. i did a quick search and found this idea
"Shipping boxes for chickens are unable to supply water due to spilling and leakage, though some shippers supply fruit such as apples or oranges. (I had a friend that shipped canaries around the world. He hot glued orange halves into clean tuna cans and hot glued the cans to the floor of the shipping box.)" from http://www.raising-chickens.org/shipping-boxes-for-chickens.html
potatoes also have a fair amount of moisture in them and might last a little longer than fruit. since his trip wont take too long either way would probably work.
I've not shipped before, but I've been watching you two on the roo. I think you have to buy a live bird shipping box. It will have lots of vent holes. I don't think you can put him in a regular box. And I was told by a person who ships to use apples and put pine shavings down in the bottom of the box.