Large Language Model (LLM)-based recommendation systems leverage powerful language models to generate personalized suggestions by processing user interactions and preferences. Unlike traditional recommendation systems that rely on structured data and collaborative filtering, LLM-based models process textual and contextual information, often using cloud-based infrastructure. This raises privacy concerns, as user data is transmitted to remote servers, increasing the risk of exposure and reducing control over personal information. To address this, we propose a hybrid privacy-preserving recommendation framework which separates sensitive from nonsensitive data and only shares the latter with the cloud to harness LLM-powered recommendations. To restore lost recommendations related to obfuscated sensitive data, we design a de-obfuscation module that reconstructs sensitive recommendations locally. Experiments on real-world e-commerce datasets show that our framework achieves almost the same recommendation utility with a system which shares all data with an LLM, while preserving privacy to a large extend. Compared to obfuscation-only techniques, our approach improves HR@10 scores and category distribution alignment, offering a better balance between privacy and recommendation quality. Furthermore, our method runs efficiently on consumer-grade hardware, making privacy-aware LLM-based recommendation systems practical for real-world use.