I have never built a boat out of cardboard, but I would make the following recommendations:
1. Use several layers of cardboard glued together with a waterproof glue to make stiff pieces of "wood". If you need curved pieces of "wood", you can make a jig and glue the pieces together in the jig so that when the glue dries, the "wood" will have the proper shape.
2. After the boat is built and glued together, paint the inside and outside with a thin layer of the glue. This should waterproof the cardboard. Paint the boat afterward to further protect the glue and waterproofing.
Good luck. Sounds like fun. And don't forget to be safe!

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Formerly a mentor with Team Stealth, 1802. Thanks, kids. It was fun!
2008 Greater Kansas City Regional Winner (Thanks 476 and 1806)

2010 Greater Kansas City Regional Gracious Professionalism Award
2012 Greater Kansas City Regional Imagery Award
"It doesn't hurt to be smart as long as you don't out-think yourself." -- Steve Fujita Former KC Chiefs player.