Computing geodesic distances on 3D surfaces is fundamental to many tasks in 3D vision and geometry processing, with deep connections to tasks such as shape correspondence. Recent learning-based methods achieve strong performance but rely on large 3D backbones, leading to high memory usage and latency, which limit their use in interactive or resource-constrained settings. We introduce LiteGE, a lightweight approach that constructs compact, category-aware shape descriptors by applying PCA to unsigned distance field (UDFs) samples at informative voxels. This descriptor is efficient to compute and removes the need for high-capacity networks. LiteGE remains robust on sparse point clouds, supporting inputs with as few as 300 points, where prior methods fail. Extensive experiments show that LiteGE reduces memory usage and inference time by up to 300x compared to existing neural approaches. In addition, by exploiting the intrinsic relationship between geodesic distance and shape correspondence, LiteGE enables fast and accurate shape matching. Our method achieves up to 1000x speedup over state-of-the-art mesh-based approaches while maintaining comparable accuracy on non-isometric shape pairs, including evaluations on point-cloud inputs. The source code and trained models are available at https://github.com/yya-111/LiteGE.