The cylindrical body of your new paper "dagger" is fairly resistant to sideways pressure, while the point can do real damage if directed against soft tissues. The strength of a single paper sheet is limited, so two or three may be used for a stronger construction. A manila envelope would be stronger yet, as the two sides are connected and the paper is thicker.
A plastic binder would be stronger yet. If a material isn't pliable enough for rolling up, folding it into a three or four sides pyramid would work as well. The flared base end would act as a pommel, keeping the hand from slipping from the impact of a stabbing motion.
A sheet of paper can be a weapon. A terrorist can use it, as can a counter-terrorist. As long as TSA is focusing on weapons, they are missing the real weapons -- the human brains. ANYTHING can be turned into an offensive weaponized tool. Unfortunately, very few tools can be improvised be defenders quickly enough to make a difference. TSA policies are further stacking the deck in favor of hijackers.