Digital microfluidics based on electrowetting-on-dielectric (EWOD) has recently emerged as one of the most promising technologies to realize integrated and highly flexible lab-on-a-chip systems. In such EWOD-based digital microfluidic devices, the aqueous droplets have traditionally been manipulated either directly in air or in an immiscible fluid such as silicone oil. However, both transporting mediums have important limitations and neither offers the flexibility required to fulfil the needs of several applications. In this paper, we report on an alternative mode of operation for EWOD-based devices in which droplets enclosed in a thin layer of oil are manipulated in air. We demonstrate the possibility to perform on-chip the fundamental fluidic operations by using such water-oil core-shell droplets and compare systematically the results with the traditional approach where the aqueous droplets are manipulated directly in air or oil. We show that the core-shell configuration combines several advantages of both the air and oil mediums. In particular, this configuration not only reduces the operation voltage of EWOD-based devices but also leads to higher transport velocities when compared with the manipulation of droplets directly in air or oil.