Rapid image acquisition for a region affected by an earthquake is important to manage the rescue operation. The use of an unmanned aerial vehicle (UAV) to rapidly cruise an affected region and obtain very high resolution (VHR) images is highly advantageous. However, haze is a problem for many UAV aerial images, especially when UAVs cross clouds. In this paper, we present a parallel predicting workflow that cooperates with Swin Transformer UNet (ST-UNet) for this task. ST-UNet utilizes the Swin Transformer instead of a convolutional layer (CNN), which greatly enhances the processing speed without accuracy loss. The predicting workflow employs parallel processing and a reasonable data structure to maximize the computing resources for rapid processing. To demonstrate the advantageousness of the proposed workflow, we employed three public remote sensing datasets for evaluation, and the proposed ST-UNet obtained the highest accuracy and speed. Furthermore, the high dehazing performance of ST-UNet was demonstrated using a real post-earthquake scene.