While magnetic hysteresis usually considers magnetic domains, the switching of the core of magnetic vortices has recently become an active topic. We considered Bloch domain walls, which are known to display at the surface of thin films flux-closure features called Néel caps. We demonstrated the controlled switching of these caps under a magnetic field, occurring via the propagation of a surface vortex. For this we considered flux-closure states in elongated micron-sized dots, so that only the central domain wall can be addressed, while domains remain unaffected.