This article addresses the challenge of vision-based proximity navigation in asteroid exploration missions and on-orbit servicing. Traditional feature extraction methods struggle with the significant appearance variations of asteroids due to limited scattered light. To overcome this, we propose a lightweight feature extractor specifically tailored for asteroid proximity navigation, designed to be robust to illumination changes and affine transformations. We compare and evaluate state-of-the-art feature extraction networks and three lightweight network architectures in the asteroid context. Our proposed feature extractors and their evaluation leverages both synthetic images and real-world data from missions such as NEAR Shoemaker, Hayabusa, Rosetta, and OSIRIS-REx. Our contributions include a trained feature extractor, incremental improvements over existing methods, and a pipeline for training domain-specific feature extractors. Experimental results demonstrate the effectiveness of our approach in achieving accurate navigation and localization. This work aims to advance the field of asteroid navigation and provides insights for future research in this domain.