Rare words remain a critical bottleneck for speech-to-text systems. While direct fine-tuning improves recognition of target words, it often incurs high cost, catastrophic forgetting, and limited scalability. To address these challenges, we propose a training-free paradigm based on task vectors for rare word recognition and translation. By defining task vectors as parameter differences and introducing word-level task vector arithmetic, our approach enables flexible composition of rare-word capabilities, greatly enhancing scalability and reusability. Extensive experiments across multiple domains show that the proposed method matches or surpasses fine-tuned models on target words, improves general performance by about 5 BLEU, and mitigates catastrophic forgetting.