The rapid growth of the Internet of Things (IoT) has led to an increased deployment of unmanned aerial vehicles (UAVs) across various sectors. However, efficiency and security issues are persistently among the primary challenges in UAV networks. In addition, significant communication delays can occur when UAVs perform remote tasks far from a command center (CC); in some cases, they may be unable to communicate with the CC. To address these challenges, in this paper, an efficient online/offline heterogeneous proxy signcryption scheme for secure communication in UAV networks (HOOPSC) is proposed. This scheme enables the CC in a certificateless cryptosystem (CLC) environment to delegate a nearby ground control station (GCS) to act as an agent, and directly send commands to the UAV within an identity-based cryptosystem (IBC) when the UAV undertakes remote tasks far from the CC. The UAV then decrypts and verifies commands for authenticity and confidentiality. In the proposed scheme, the signcryption process is split into offline and online phases, with most of the heavy computations conducted without the availability of the messages during the offline phase. Only light computations are performed in the online phase when a message is available. Moreover, a formal security proof is given in a random oracle model. Finally, a performance analysis reveals that HOOPSC outperforms existing relevant schemes, making it ideal for long-range operations in UAV networks.