Moisture cures super glue incredibly quickly. This is (partially) why smooth dry surfaces like glass take a very long time to glue, but fingers are instant. Some glues even recommend very lightly wetting the surfaces being joined to help with fast adhesion.

Acetone will dissolve cyanoacrylate very quickly and can be purchased in bulk from any hardware store for cheap. Acetone is also the primary component in most fingernail polish remover, so that can also be used in a pinch.