Deep observations of galaxy outskirts reveal faint extended stellar components (ESCs) of streams, shells, and halos, which are ghostly remnants of the tidal disruption of satellite galaxies. We use cosmological galaxy formation simulations in Cold Dark Matter (CDM) and Warm Dark Matter (WDM) models to explore how the dark matter model influences the spatial, kinematic, and orbital properties of ESCs. These reveal that the spherically averaged stellar mass density at large galacto-centric radius can be depressed by up to a factor of 10 in WDM models relative to the CDM model, reflecting the anticipated suppressed abundance of satellite galaxies in WDM models. However, these differences are much smaller in WDM models that are compatible with observational limits, and are comparable in size to the system-to-system variation we find within the CDM model. This suggests that it will be challenging to place limits on dark matter using only the unresolved ESC.