Fully-supervised airway segmentation has accomplished significant triumphs over the years in aiding pre-operative diagnosis and intra-operative navigation. However, full voxel-level annotation constitutes a labor-intensive and time-consuming task, often plagued by issues such as missing branches, branch annotation discontinuity, or erroneous edge delineation. label-efficient solutions for airway extraction are rarely explored yet primarily demanding in medical practice. To this end, we introduce a novel skeleton-level annotation (SkA) tailored to the airway, which simplifies the annotation workflow while enhancing annotation consistency and accuracy, preserving the complete topology. Furthermore, we propose a skeleton-supervised learning framework to achieve accurate airway segmentation. Firstly, a dual-stream buffer inference is introduced to realize initial label propagation from SkA, avoiding the collapse of direct learning from SkA. Then, we construct a geometry-aware dual-path propagation framework (GDP) to further promote complementary propagation learning, composed of hard geometry-aware propagation learning and soft geometry-aware propagation guidance. Experiments reveal that our proposed framework outperforms the competing methods with SKA, which amounts to only 1.96% airways, and achieves comparable performance with the baseline model that is fully supervised with 100% airways, demonstrating its significant potential in achieving label-efficient segmentation for other tubular structures, such as vessels.