Drones operating in complex environments face a significant threat from thin obstacles, such as steel wires and kite strings at the submillimeter level, which are notoriously difficult for conventional sensors like RGB cameras, LiDAR, and depth cameras to detect. This paper introduces SkyShield, an event-driven, end-to-end framework designed for the perception of submillimeter scale obstacles. Drawing upon the unique features that thin obstacles present in the event stream, our method employs a lightweight U-Net architecture and an innovative Dice-Contour Regularization Loss to ensure precise detection. Experimental results demonstrate that our event-based approach achieves mean F1 Score of 0.7088 with a low latency of 21.2 ms, making it ideal for deployment on edge and mobile platforms.