Word Sense Disambiguation (WSD) aims to determine the correct meaning of a word in context from a predefined inventory, and remains a fundamental challenge in natural language understanding. Existing methods rely heavily on manually annotated data, which limits coverage and generalization. In this work, we propose a scalable framework that leverages large language models (LLMs) as knowledge distillers to construct silver-standard WSD corpora. We explore generation-based distillation, where diverse examples are synthesized for dictionary senses, and annotation-based distillation, where LLMs assign sense labels to polysemous words within real-world corpus sentences. The resulting data is used to train tiny models. Extensive experiments show that models distilled from LLM-generated data outperform those trained on gold-standard corpora, especially on general-domain benchmarks. Our annotation-based model, after balancing sense distribution, achieves 50% F1 gain on the most challenging test set and the best distilled model can match or even exceed the performance of its LLM teacher, despite having over 1000 times fewer parameters. These results demonstrate the effectiveness of LLM-based distillation for building accurate, generalizable, and efficient WSD systems.