I imagine that such a spherical wormhole could theoretically be detected by watching for light reflecting off objects despite a lack of nearby stars. For example, if we trace the path of light passing through a wormhole and reflecting off a planet back to its origin, it would look like that light is coming from empty space. Like the beam of light coming out of a recessed lighting fixture in your ceiling, it would be directional and you'd only be able to see the lightbulb if you're standing directly under it, otherwise you can only infer the existence of the lightbulb and recessed hole in the ceiling by observing the light reflecting off the floor.
I do wonder what happens to space-time at the points between wormhole terminations. In the folded paper analogy, someone had to apply enough energy to manipulate the position of every atom in the paper as they were bending it over on itself, and at the end there would be a dramatically different shape to the paper between those two points.