Unmanned aerial vehicles (UAVs) operating as aerial base stations in open airspace face inherent security vulnerabilities during data transmission, particularly from eavesdroppers. To address this, this paper proposes a coordinated multi-point (CoMP) UAV-assisted network architecture to enhance downlink transmission security. The network space is tessellated into equal-sized hexagonal cells, where UAVs within each cell jointly serve ground users. Using stochastic geometry, we develop an analytical framework to characterize the downlink secrecy rate performance. Key metrics—including coverage probability, transmission rate, and average secrecy rate (ASR)—are derived in closed form. Our analysis quantifies the impact of critical system parameters on security performance. Simulations validate the analytical model, demonstrating close alignment between numerical and theoretical results. Notably, the proposed CoMP scheme achieves a 41.2% higher ASR compared to non-cooperative benchmark, significantly improving communication security.