Large reasoning models achieve strong performance through reinforcement learning but can suffer safety degradation. External teacher distillation can restore safety yet may compromise reasoning performance. We formalize safety realignment as a KL projection: the student's native filter-accepted distribution is uniquely KL-optimal, while teacher targets incur excess KL when they differ. Guided by this analysis, we propose ThinkSafe, which generates safety-alignment data from the frozen student without external teachers. Refusal steering elicits safety reasoning, and a safety guard filters the responses before offline fine-tuning. Our analysis bounds steering-induced target distortion and gives a sufficient condition for lower average target KL than teacher distillation. Experiments on DeepSeek-R1-Distill and Qwen3 show substantial safety improvements with competitive reasoning performance. On Qwen3-0.6B, ThinkSafe achieves better safety and comparable reasoning to GRPO in about one-seventh of the wall-clock time, including data generation. Code, models, and datasets are available at https://github.com/seanie12/ThinkSafe and https://huggingface.co/Seanie-lee/collections.

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