The motion of a classical particle is described by a curve in spacetime. In situations like the twin paradox, we don't care about the small differences between the motions of different component parts of the same object, so we treat all clocks, humans, spaceships etc., as particles. The motion of each object is then approximately described by a curve in spacetime.
One of the axioms of both SR and GR is that a clock measures the proper time of the curve that represents its motion. The twin paradox is just a scenario where two objects move as described by two different curves with the same endpoints. The standard twin paradox considers two curves in Minkowski spacetime, but if you want to consider another spacetime, that's fine. There is however no spacetime in which two objects are brought together without movement. No matter what coordinate system you're using, one of the objects is moving.
If one of the two twins leaves Earth the usual way, and returns through a wormhole, the curve that describes his motion can have a longer or shorter proper time than it would have had otherwise. Either way, you find that guy's final age by calculating the proper time of the curve that represents his motion.
