The folded piece of paper abstraction is meant merely as a demonstration of the wormhole concept, basically warping spacetime to shorten the XYZ distance between to points. It was not meant to be a realistic engineering plan on how to do accomplish that feat (which is the way you are conceptualizing it).
Remember, spacetime is naturally warped by masses, particularly large masses; think of how Eddington provided the key evidence for Einstein's General Relativity by capturing the light of a distance star bending around the Sun. Even your mass, although insignificant compared to the Sun, is massive compared to a subatomic particle, and bends spacetime towards yourself ever so slightly.
Also, remember that E=MC^2. This tells us two things: 1) mass and energy are essentially different versions of the same thing (think ice and water being different version of H2O) and 2) one needs a massive amount of energy to equal the equivalent of mass.
So, while the Sun can easily bend light from a distant star, it would require a massive amount of energy to bend that same light in the same manner. Now, from a human perspective, would not be able to pass through a wormhole created via mass (it would be no different than trying to go through a brick wall). Thus, we would need a wormhole made via energy. Thus, we would need to concentrate a massive amount of energy into a very, very, small area (a quantum-sized area). It would require more energy than we could ever conceivably produce in the next 100 years given the current pace of technology (and remember E=MC^2, which means we would need a massive amount of mass to fuel that energy).
On top of the outlined above, even if we were able to produce enough energy to create a quantum wormhole, control and manipulate that wormhole to increase the size enough for us to pass through, we would still not be able to (in theory) control where it comes out at (maybe we will, one day, have quantum mechanics/fluctuations/entanglement figured out in order to change this).