We demonstrate that a magnetic field-free two-pulse scheme previously proposed to switch an in-plane magnetized free layer is also suitable for switching a perpendicularly magnetized layer. In the case of a symmetric square free layer, deterministic switching is achieved by running the second pulse over a part of the free layer. Applying the same approach to a rectangular free layer results in switching times as short as 0.25 ns. The optimal overlap of the second heavy metal wire with the free layer is found to be between 30-60%. It is shown that the switching scheme yields a large window for the time delay/overlap between the two pulses, still maintaining the switching times as short as 0.25 ns. Consequently, the scheme is extremely robust against pulse duration fluctuations and pulse synchronization failures.