Zero-shot skeleton-based action recognition (ZS-SAR) is fundamentally constrained by prevailing approaches that rely on aligning skeleton features with static, class-level semantics. This coarse-grained alignment fails to bridge the domain shift between seen and unseen classes, thereby impeding the effective transfer of fine-grained visual knowledge. To address these limitations, we introduce \textbf{DynaPURLS}, a unified framework that establishes robust, multi-scale visual-semantic correspondences and dynamically refines them at inference time to enhance generalization. Our framework leverages a large language model to generate hierarchical textual descriptions that encompass both global movements and local body-part dynamics. Concurrently, an adaptive partitioning module produces fine-grained visual representations by semantically grouping skeleton joints. To fortify this fine-grained alignment against the train-test domain shift, DynaPURLS incorporates a dynamic refinement module. During inference, this module adapts textual features to the incoming visual stream via a lightweight learnable projection. This refinement process is stabilized by a confidence-aware, class-balanced memory bank, which mitigates error propagation from noisy pseudo-labels. Extensive experiments on three large-scale benchmark datasets, including NTU RGB+D 60/120 and PKU-MMD, demonstrate that DynaPURLS significantly outperforms prior art, setting new state-of-the-art records. The source code is made publicly available at https://github.com/Alchemist0754/DynaPURLS