Schema matching is a critical task in data integration, particularly in the medical domain where disparate Electronic Health Record (EHR) systems must be aligned to standard models like OMOP CDM. While Large Language Models (LLMs) have shown promise in schema matching, they suffer from hallucination and lack of up-to-date domain knowledge. Knowledge Graphs (KGs) offer a solution by providing structured, verifiable knowledge. However, existing KG-augmented LLM approaches often rely on inefficient complex multi-hop queries or storage-intensive vector-based retrieval methods. This paper introduces SMoG (Schema Matching on Graph), a novel framework that leverages iterative execution of simple 1-hop SPARQL queries, inspired by successful strategies in Knowledge Graph Question Answering (KGQA). SMoG enhances explainability and reliability by generating human-verifiable query paths while significantly reducing storage requirements by directly querying SPARQL endpoints. Experimental results on real-world medical datasets demonstrate that SMoG achieves performance comparable to state-of-the-art baselines, validating its effectiveness and efficiency in KG-augmented schema matching.