Large language model (LLM) embeddings offer a promising new avenue for database query optimization. In this paper, we explore how pre-trained execution plan embeddings can guide SQL query execution without the need for additional model training. We introduce LLM-PM (LLM-based Plan Mapping), a framework that embeds the default execution plan of a query, finds its k nearest neighbors among previously executed plans, and recommends database hintsets based on neighborhood voting. A lightweight consistency check validates the selected hint, while a fallback mechanism searches the full hint space when needed. Evaluated on the JOB-CEB benchmark using OpenGauss, LLM-PM achieves an average speed-up of 21% query latency reduction. This work highlights the potential of LLM-powered embeddings to deliver practical improvements in query performance and opens new directions for training-free, embedding-based optimizer guidance systems.