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The integration of unmanned aerial vehicles (UAVs) into the terrestrial cellular networks is envisioned as one key technology for next-generation wireless communications. In this work, we consider the physical layer security of the communications links in the millimeter-wave (mmWave) spectrum which are maintained by UAVs functioning as base stations (BS). In particular, we propose a new precoding strategy which incorporates the channel state information (CSI) of the eavesdropper (Eve) compromising link security. We show that our proposed precoder strategy eliminates any need for artificial noise (AN) transmission in underloaded scenarios (fewer users than number of antennas). In addition, we demonstrate that our nonlinear precoding scheme provides promising secrecy-rate performance even for overloaded scenarios at the expense of transmitting low-power AN.