This study explores the potential of biomimetic vibrissal sensors for tactile navigation in aerial robotics. Inspired by the sophisticated sensory system of rodents, we developed a non-intrusive, whisker-based tactile sensor system integrated into a drone platform. The system enables real-time detection and navigation through complex environments by emulating the tactile perception capabilities of natural whiskers. Our approach includes a novel platform design for easy sensor integration, a preprocessing solution to mitigate signal distortion as well as a simple static calibration set-up to estimate normal contact distances. The effectiveness of the system was validated through contour following tasks, where the whisker sensors provided feedback for precise navigation along surfaces with varying orientations. Results demonstrate that our system can estimate normal distances and wall orientations with sufficient accuracy, despite challenges such as lateral slip. This research highlights the potential of whisker-inspired sensors in enhancing the tactile sensing capabilities of aerial robots, offering significant advantages over traditional tactile sensors in terms of weight, power consumption, and operational flexibility in diverse environmental conditions.