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This work investigates the spherically symmetric thin-shell wormhole solutions in four-dimensional Einstein-Gauss-Bonnet theory and explores their stabilities under radial, linear perturbations. These solutions are typically traversable and characterized by a thin-shell throat in accordance with Israel's junction conditions. In asymptotically flat and AdS spacetimes with a negative Gauss-Bonnet coupling constant, stable neutral wormholes are encountered when the magnitude of the coupling constant becomes significant. The throats of such wormholes are sustained by ordinary matter and possess finite radii. In asymptotically dS spacetimes, no stable neutral wormhole featuring ordinary matter is observed. On the other hand, for positive Gauss-Bonnet coupling constant, stable thin-shell wormhole solutions can be established when the throats are exclusively supported by exotic matter. Moreover, stable charged wormholes comprised of ordinary matter are found universally in the asymptotically flat, AdS, and dS spacetimes. Unlike their neutral counterparts, the throat radii of such charged wormholes can be arbitrarily small. However, as the charge becomes more significant, such solutions only remain stable when supported by exotic matter.