Is it possible to make a scissor-like hinge out of cardboard?
Small brass eyelets could be quite durable in this application.



These are sold for card-making and scrapbooking and used to appear on certain kinds of office supplies in very similar applications. They might also be sold at leather crafting outlets.

They would require a hole be punched in the cardboard first, for best wear characteristics. Also, how far you set them is critical to getting the right resistance to rotation of the two cardboard pieces.

Their use requires a punch and die that would be sold at the same place for a few dollars. It's possible there is a pliers-like version as well.