Speculative decoding accelerates large language model (LLM) inference by allowing a small draft model to predict multiple future tokens for verification by a larger target model. In AI-native radio access networks (AI-RAN), this enables device-edge collaborative inference but introduces significant uplink overhead, as existing distributed speculative decoding schemes transmit full vocabulary logits at every step. We propose a sparsify-then-sample strategy, Truncated Sparse Logits Transmission (TSLT), which transmits only the logits and indices of a truncated candidate set. We provide theoretical guarantees showing that the acceptance rate is preserved under TSLT. TSLT is further extended to multi-candidate case, where multiple draft candidates per step increase acceptance probability. Experiments show that TSLT significantly reduces uplink communication while maintaining end-to-end inference latency and model quality, demonstrating its effectiveness for scalable, communication-efficient distributed LLM inference in future AI-RAN systems.