Recent advancements in large language models (LLMs) have boosted research on generating SQL queries from domain-specific questions, particularly in the medical domain. A key challenge is detecting and filtering unanswerable questions. Existing methods often relying on model uncertainty, but these require extra resources and lack interpretability. We propose a lightweight model that predicts relevant database schemas to detect unanswerable questions, enhancing interpretability and addressing the data imbalance in binary classification tasks. Furthermore, we found that LLM-generated schema descriptions can significantly enhance the prediction accuracy. Our method provides a resource-efficient solution for unanswerable question detection in domain-specific question answering systems.