Consumer electronics can support sixth-generation (6G) systems and their services, including ultra-reliable and low-latency communications (URLLC). In this context, unmanned aerial vehicles (UAVs) have become increasingly popular because they can: be dynamically positioned, take advantage of channel gains, and communicate directly via line-of-sight. UAVs, on the other hand, are unable to maintain a stable flight for prolonged periods of time and suffer from jittering impairments caused by strong winds. As a result of atmospheric conditions and environmental interference, the perfect channel state information (CSI) becomes obsolete. The aim of this study is to propose a power-efficient resource allocation scheme for URLLC-enabled UAV communication systems under finite block lengths, imperfect CSIs, and adverse jittering effects caused by wind. This involves optimizing UAV positioning and blocklength distribution together. Additionally, we propose a perturbation-based semidefinite programming (SDP) approach to reduce the sum power and demonstrate that it outperforms fixed benchmark algorithms. As such, it can reach power savings up to $77.18\%$ compared to fixed benchmark algorithms. Our extensive simulation results demonstrate that our approach performs similarly to the exhaustive search and has low complexity. Thus, the proposed method thus provides a practical power-efficient URLLC implementation for memory-constrained UAV networks.