The dynamics of transient liquid beryllium flows induced on the ITER first wall during the current quench stage of unmitigated vertical displacement events are modelled by means of two-dimensional Navier-Stokes simulations. The study focuses on melt that is driven to the first wall panels' chamfered edges, where free-surface instabilities are the most likely to be seeded. Beyond their impact on plasma-facing component damage, these instabilities potentially result in material ejection in the form of droplets, which may ultimately solidify into dust and accumulate in the vessel. Based on prior integrated numerical predictions of quenching magnetic equilibria, wall energy deposition and melt-related damage in a concrete worst-case disruption scenario, the simulations suggest that, although the liquid layer is significantly destabilized, only 5% of the total melt mass created on the wall surface is lost through ejection. This result can serve as a basis to refine the estimates of the real transient-induced beryllium dust inventory expected in ITER.