The motion and temperature evolution of beryllium droplets produced by first wall surface melting after ITER major disruptions and vertical displacement events mitigated during the current quench are simulated by the MIGRAINe dust dynamics code. These simulations employ an updated physical model which addresses droplet-plasma interaction in ITER-relevant regimes characterized by magnetized electron collection and thin-sheath ion collection, as well as electron emission processes induced by electron and high-Z ion impacts. The disruption scenarios have been implemented from DINA simulations of the time-evolving plasma parameters, while the droplet injection points are set to the first-wall locations expected to receive the highest thermal quench heat flux according to field line tracing studies. The droplet size, speed and ejection angle are varied within the range of currently available experimental and theoretical constraints, and the final quantities of interest are obtained by weighting single-trajectory output with different size and speed distributions. Detailed estimates of droplet solidification into dust grains and their subsequent deposition in the vessel are obtained. For representative distributions of the droplet injection parameters, the results indicate that at most a few percents of the beryllium mass initially injected is converted into solid dust, while the remaining mass either vaporizes or forms liquid splashes on the wall. Simulated in-vessel spatial distributions are also provided for the surviving dust, with the aim of providing guidance for planned dust diagnostic, retrieval and clean-up systems on ITER.