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Recently, it has been shown that a vertical displacement event (VDE) can occur in ITER even when the walls are perfect conductors, as a consequence of the current quench [A. H. Boozer, Physics of Plasmas 26 114501 (2019)]. We used the extended-MHD code M3D-C1 with an ITER-like equilibrium and induced a current quench to explore cold VDEs in the limit of perfectly conducting walls, using different wall geometries. In the particular case of a rectangular wall with the side walls far away from the plasma, we obtained very good agreement with the analytical model developed by Boozer that considers a top/bottom flat-plates wall. We show that the solution in which the plasma stays at the initial equilibrium position is improved when bringing the side walls closer to the plasma. When using the ITER first wall in the limit of a perfect conductor, the plasma stays stable at the initial equilibrium position far beyond the value predicted by the flat-plates wall limit. On the other hand, when considering the limit in which the inner shell of the ITER vacuum vessel is acting as a perfect conductor, the plasma is displaced during the current quench but the edge safety factor stays above $2$ longer in the current decay compared to the flat-plates wall limit. In all the simulated cases, the vertical displacement is found to be strongly dependent on the plasma current, in agreement with a similar finding in the flat-plates wall limit, showing an important difference with usual VDEs in which the current quench is not a necessary condition.