Unmanned aerial vehicles (UAVs) have been applied to various tasks in the low-altitude economy (LAE) with the advantages of high mobility, low costs, and flexible deployment. However, due to the broadcast nature of wireless channels and the increasing number of UAVs, the security of UAV control information and the spectrum resource utilization face significant challenges and threats. Therefore, in this paper, we investigate the secrecy performance of UAV short-packet control information transmission networks based on rate-splitting multiple access (RSMA) with the presence of multiple eavesdroppers. Moreover, we consider and analyze the impacts of both imperfect channel state information (CSI) and successive interference cancellation (SIC) in a more realistic scenario. Considering both large-scale fading and Nakagami-m small-scale fading, the closed-form expression of the average effective secrecy sum rate is derived utilizing stochastic geometry and the Gauss-Chebyshev quadrature. Considering that the private stream can be concealed within the high-power common stream, an optimization problem is formulated to maximize the common rate by jointly optimizing the blocklength and power allocation coefficients to enhance security. The block coordinate descent (BCD) algorithm is adopted to solve this problem. Finally, simulation results demonstrate the accuracy of the analysis and the effectiveness of the proposed scheme.