We consider a relay system empowered by an unmanned aerial vehicle (UAV) that facilitates downlink information delivery while adhering to finite blocklength requirements. The setup involves a remote controller transmitting information to both a UAV and an industrial Internet of Things (IIoT) or remote device, employing the non-orthogonal multiple access (NOMA) technique in the first phase. Subsequently, the UAV decodes and forwards this information to the remote device in the second phase. Our primary objective is to minimize the decoding error probability (DEP) at the remote device, which is influenced by the DEP at the UAV. To achieve this goal, we optimize the blocklength, transmission power, and location of the UAV. However, the underlying problem is highly non-convex and generally intractable to be solved directly. To overcome this challenge, we adopt an alternative optimization (AO) approach and decompose the original problem into three sub-problems. This approach leads to a sub-optimal solution, which effectively mitigates the non-convexity issue. In our simulations, we compare the performance of our proposed algorithm with baseline schemes. The results reveal that the proposed framework outperforms the baseline schemes, demonstrating its superiority in achieving lower DEP at the remote device. Furthermore, the simulation results illustrate the rapid convergence of our proposed algorithm, indicating its efficiency and effectiveness in solving the optimization problem.