根据输入敏感度动态分配计算任务，兼顾隐私与效率。

Large Language Models (LLMs) demonstrate impressive capabilities in natural language understanding and generation, but incur high communication overhead and privacy risks in cloud deployments, while facing compute and memory constraints when confined to edge devices. Cloud-edge inference has emerged as a promising paradigm for improving privacy in LLM services by retaining sensitive computations on local devices. However, existing cloud-edge inference approaches apply uniform privacy protection without considering input sensitivity, resulting in unnecessary perturbation and degraded utility even for non-sensitive tokens. To address this limitation, we propose Privacy-aware Routing for Inference with Semantic Modulation (PRISM), a context-aware framework that dynamically balances privacy and inference quality. PRISM executes in four stages: (1) the edge device profiles entity-level sensitivity; (2) a soft gating module on the edge selects an execution mode - cloud, edge, or collaboration; (3) for collaborative paths, the edge applies adaptive two-layer local differential privacy based on entity risks; and (4) the cloud LLM generates a semantic sketch from the perturbed prompt, which is then refined by the edge-side small language model (SLM) using local context. Our results show that PRISM consistently achieves superior privacy-utility trade-offs across various scenarios, reducing energy consumption and latency to 40-50% of baseline methods such as Uniform and Selective LDP, while maintaining high output quality under strong privacy constraints. These findings are validated through comprehensive evaluations involving realistic prompts, actual energy measurements, and heterogeneous cloud-edge model deployments.