Vision-and-Language Navigation (VLN) poses significant challenges for agents to interpret natural language instructions and navigate complex 3D environments. While recent progress has been driven by large-scale pre-training and data augmentation, current methods still struggle to generalize to unseen scenarios, particularly when complex spatial and temporal reasoning is required. In this work, we propose SkillNav, a modular framework that introduces structured, skill-based reasoning into Transformer-based VLN agents. Our method decomposes navigation into a set of interpretable atomic skills (e.g., Vertical Movement, Area and Region Identification, Stop and Pause), each handled by a specialized agent. To support targeted skill training without manual data annotation, we construct a synthetic dataset pipeline that generates diverse, linguistically natural, skill-specific instruction-trajectory pairs. We then introduce a novel training-free Vision-Language Model (VLM)-based router, which dynamically selects the most suitable agent at each time step by aligning sub-goals with visual observations and historical actions. SkillNav obtains competitive results on commonly used benchmarks, and establishes state-of-the-art generalization to the GSA-R2R, a benchmark with novel instruction styles and unseen environments.