The chemical products mentioned so far will stay in the cardboard and paper. Your best bet is steam. Only, try and practice with a piece of mail that has a label on it first, since you can easily warp the paper if done incorrectly. For the cardboard I wouldn't worry about warping.
You can use a teapot for concentrated steam.
P.S. -- If you do get some warping, don't worry, just iron the paper in between two pieces of cloth.