The increasing adoption of large language models (LLMs) in cloud-based services has raised significant privacy concerns, as user inputs may inadvertently expose sensitive information. Existing text anonymization and de-identification techniques, such as rule-based redaction and scrubbing, often struggle to balance privacy preservation with text naturalness and utility. In this work, we propose a zero-shot, tree-search-based iterative sentence rewriting algorithm that systematically obfuscates or deletes private information while preserving coherence, relevance, and naturalness. Our method incrementally rewrites privacy-sensitive segments through a structured search guided by a reward model, enabling dynamic exploration of the rewriting space. Experiments on privacy-sensitive datasets show that our approach significantly outperforms existing baselines, achieving a superior balance between privacy protection and utility preservation.