Reinforcement learning sharpens LLM reasoning, but parameter updates are expensive, forgetful, and opaque; training-free libraries swap gradients for a textual store but still use trajectory-level, correlation-based admission and flat structure. To address both, we propose HyperSkill, a Training-Free Omnimodal GRPO framework that keeps the backbone frozen and replaces gradient updates with auditable edits to a Hypergraph-Indexed Skill-Library, where skills are advantage-bearing nodes and compositions are hyperedges. It has three components: training-time distillation admits counterfactually checked skills and learns a protocol skill from failures; gated hypergraph retrieval injects advantage-ranked skills where a per-dataset gate admits them; and an execution protocol makes the frozen backbone commit to an answer. On 11 text, vision-language, and omnimodal benchmarks, HyperSkill is best or tied on every dataset and beats the best baseline by 13.0 average F1 points while keeping the backbone frozen. Our software and data are publicly available at https://github.com/LHRLAB/HyperSkill.

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