Recent years have witnessed growing interest in adopting large language models (LLMs) for Register Transfer Level (RTL) code optimization. While powerful cloud-based LLMs offer superior optimization capabilities, they pose unacceptable intellectual property (IP) leakage risks when processing proprietary hardware designs. In this paper, we propose a new scenario where Verilog code must be optimized for specific attributes without leaking sensitive IP information. We introduce the first IP-preserving edge-cloud collaborative framework that leverages the benefits of both paradigms. Our approach employs local small LLMs (e.g., Qwen-2.5-Coder-7B) to perform secure comparative analysis between paired high-quality target designs and novice draft codes, yielding general design principles that summarize key insights for improvements. These principles are then used to query stronger cloud LLMs (e.g., Deepseek-V3) for targeted code improvement, ensuring that only abstracted and IP-safe guidance reaches external services. Our experimental results demonstrate that the framework achieves significantly higher optimization success rates compared to baseline methods. For example, combining Qwen-2.5-Coder-7B and Deepseek-V3 achieves a 66.67\% optimization success rate for power utilization, outperforming Deepseek-V3 alone (49.81\%) and even commercial models like GPT-4o (55.81\%). Further investigation of local and cloud LLM combinations reveals that different model pairings exhibit varying strengths for specific optimization objectives, with interesting trends emerging when varying the number of comparative code pairs. Our work establishes a new paradigm for secure hardware design optimization that balances performance gains with IP protection.