Large Language Models remain vulnerable to adversarial prompts that elicit toxic content even after safety alignment. We present ToxSearch, a black-box evolutionary framework that tests model safety by evolving prompts in a synchronous steady-state loop. The system employs a diverse set of operators, including lexical substitutions, negation, back-translation, paraphrasing, and two semantic crossover operators, while a moderation oracle provides fitness guidance. Operator-level analysis shows heterogeneous behavior: lexical substitutions offer the best yield-variance trade-off, semantic-similarity crossover acts as a precise low-throughput inserter, and global rewrites exhibit high variance with elevated refusal costs. Using elite prompts evolved on LLaMA 3.1 8B, we observe practically meaningful but attenuated cross-model transfer, with toxicity roughly halving on most targets, smaller LLaMA 3.2 variants showing the strongest resistance, and some cross-architecture models retaining higher toxicity. These results suggest that small, controllable perturbations are effective vehicles for systematic red-teaming and that defenses should anticipate cross-model reuse of adversarial prompts rather than focusing only on single-model hardening.