We present a simplified and fast method for simulating minor mergers between galaxy clusters. Instead of following the evolution of the dark matter haloes directly by the N-body method, we employ a rigid potential approximation for both clusters. The simulations are run in the rest frame of the more massive cluster and account for the resulting inertial accelerations in an optimized way. We test the reliability of this method for studies of minor merger induced gas sloshing by performing a one-to-one comparison between our simulations and hydro+N-body ones. We find that the rigid potential approximation reproduces the sloshing-related features well except for two artefacts: the temperature just outside the cold fronts is slightly overpredicted, and the outward motion of the cold fronts is delayed by typically 200 Myr. We discuss reasons for both artefacts.