Large Language Models enable flexible natural-language planning but remain unreliable in determinism-critical domains due to their probabilistic nature. This limitation is especially problematic in running planning, where violating safety rules can lead to safety risks. We propose SafeRun, a framework for deterministic LLM-based planning via a decoupled architecture. SafeRun separates soft interpretation by an LLM from hard constraint enforcement by a deterministic solver, ensuring strict safety constraints while preserving natural-language flexibility. To validate SafeRun, we build a comprehensive benchmark for running planning under realistic physiological and safety constraints. Experiments across five LLMs show that SafeRun achieves 100\% safety score (vs.\ 79.1\% PE average and 97.6\% CodeAct average) while maintaining competitive instruction-following scores. The SafeRun benchmark is publicly available at \href{https://huggingface.co/datasets/zzp-seeker/SafeRun-RunPlanning-Benchmark}{huggingface}.