Firstly, take my tip and don't do it! Hawking thinks it could be deleterious to your health; you would probably emerge from the other end in the form of a burst of incoherent radiation, if at all.

As for the technical problems, the main one as I see it would be that you would need to overcome the second law of thermodynamics, which is what you would need to concentrate the distributed energy of the universe in a relatively small space.

If you could manage that on even a small scale, say with the energy of a few icebergs, or the surface of a desert or two, never mind galaxies or universes, you could afford to ignore anything as boring as a wormhole, even one that would let you travel through it unharmed.