Benefiting from the deployment flexibility and the line-of-sight (LoS) channel conditions, unmanned aerial vehicle (UAV) has gained tremendous attention in data collection for wireless sensor networks. However, the high-quality air-ground channels also pose significant threats to the security of UAV aided wireless networks. In this paper, we propose a short-packet secure UAV-aided data collection and transmission scheme to guarantee the freshness and security of the transmission from the sensors to the remote ground base station (BS). First, during the data collection phase, the trajectory, the flight duration, and the user scheduling are jointly optimized with the objective of maximizing the energy efficiency (EE). To solve the non-convex EE maximization problem, we adopt the first-order Taylor expansion to convert it into two convex subproblems, which are then solved via successive convex approximation. Furthermore, we consider the maximum rate of transmission in the UAV data transmission phase to achieve a maximum secrecy rate. The transmit power and the blocklength of UAV-to-BS transmission are jointly optimized subject to the constraints of eavesdropping rate and outage probability. Simulation results are provided to validate the effectiveness of the proposed scheme.