I think I'd go with closed hulls rather than sit-in hulls because of the flexibility of the cardboard. Something slender like a catamaran hull. You could even build in some bulkheads to keep the hull stiff where you plan to sit. The bulkheads could also be used to make multiple watertight compartments to reduce your chances of sinking. Then I think I'd add an outrigger of some sort. Sit on the main hull and paddle away.

Do we get to see pictures of the result?