Cooperative ad hoc unmanned aerial vehicle (UAV) networks need essential security services to ensure their communication security. Cryptography, as the inseparable tool for providing security services, requires a robust key management system. Alas, the absence of infrastructure in cooperative networks leads to the infeasibility of providing conventional key management systems. Key pre-distribution schemes have shown promising performance in different cooperative networks due to their lightweight nature. However, intermediate decryption-encryption (DE) steps and the lack of key updates are the most concerning issues they suffer from. In this paper, we propose a simple and effective key management algorithm inspired by the idea of key pre-distribution, where it utilizes the highly dynamic UAV node movement in 3D space to provide the key update feature and optimizes the number of intermediate DE steps. Although it is a general model for any mobile ad hoc network, we have selected UAV network as an example domain to show the efficiency of the model given the high mobility. We define the communication density parameter to analytically show that using any highly dynamic random movement pattern leads our algorithm to work effectively. To show the proposed algorithm's effectiveness, we exhaustively analyze its security and performance in the UAV network using the ns-3 network simulator. Results validate our analytical findings and show how the highly dynamic UAV network movement helps our algorithm to provide the key update feature and to optimize the number of DE steps.