In long-context Large Language Model (LLM) inference, the Time-To-First-Token (TTFT) latency incurred by the prefill stage has become the foremost bottleneck limiting interactive performance and deployment cost. KV Cache reuse offers a direct path to reduce redundant prefill, yet traditional prefix caching applies only to strict-prefix scenarios; directly reusing KV Cache in non-prefix settings breaks the cross-chunk global attention relationships and causes significant degradation in generation quality. When reusable KV Cache is offloaded to GPU-external cache pools, I/O overheads across heterogeneous hardware tiers further emerge as a new TTFT bottleneck. Efficient non-prefix KV Cache reuse therefore requires both semantic-consistency recovery and compute-I/O co-optimization. This paper presents CacheTune, a frequency-guided and hardware-aware KV Cache reuse system for long-context LLM serving. CacheTune first identifies, offline, the KV pairs most critical to cross-attention recovery through frequency-domain analysis, and then selectively recomputes only these semantic-critical tokens online while reusing the remaining KVs. To turn this semantic selection into end-to-end latency reduction, CacheTune further combines sparse KV transfer, multi-stream asynchronous overlap, deferred positional-encoding recovery, and hardware-aware adaptive recomputation-ratio tuning to balance computation and data movement across heterogeneous cache pools. Evaluations on mainstream LLMs and long-context tasks show that CacheTune achieves 3.72x-4.86x TTFT speedup and 3.93x-6.21x higher throughput while maintaining generation quality close to full recompute. Even when caches are offloaded to I/O-bound SSD/HDD storage, CacheTune sustains 2.34x-2.36x TTFT speedup through adaptive recomputation.