While distributed device-edge speculative decoding enhances resource utilization across heterogeneous nodes, its performance is often bottlenecked by conventional token-level verification strategies. Such rigid alignment leads to excessive rejections, significantly diminishing the accepted sequence length and increasing interaction rounds under fluctuating wireless conditions. In this paper, we propose WISV (Wireless-Informed Semantic Verification), a novel distributed speculative decoding framework that goes beyond strict token-level matching via a channel-aware semantic acceptance policy. WISV integrates a lightweight decision head into the edge-side target LLM to dynamically evaluate speculative tokens by synthesizing high-dimensional hidden representations with instantaneous channel state information (CSI). To optimize the trade-off between verification fidelity and communication overhead, we further design two tailored communication protocols: full-hidden upload and mismatch-first selective-hidden upload. Extensive simulations using a 1B drafter and an 8B target model demonstrate that WISV achieves up to a 60.8% increase in accepted length, a 37.3% reduction in interaction rounds, and a 31.4% improvement in end-to-end latency compared to vanilla speculative decoding across tested settings, while maintaining a negligible task accuracy drop (<1%). Finally, we validate WISV on a hardware testbed comprising an NVIDIA Jetson AGX Orin and an A40-equipped server, confirming its real-world efficacy in accelerating edge-deployed LLM inference.