Translating song lyrics while preserving singability requires satisfying musical constraints, including syllable counts, rhyme schemes, and syllable patterns, that standard machine translation ignores. We present a framework that exposes IPA-based phonetic analysis as a suite of composable Agent Skills, each defined by a natural-language description plus deterministic verification scripts that the orchestrating LLM invokes on demand. The agent extracts constraints from source lyrics, then translates through a multi-phase process, calling skills to verify syllable counts and rhyme and iteratively refine syllable-count mismatches. We formalize the three musical constraints, describe the IPA skill suite and agent architecture, and propose three evaluation metrics: Syllable Error Rate (SER), Syllable Count Relative Error (SCRE), and Adjusted Rand Index (ARI). Experiments across three frontier orchestrators, with component ablations, confirm that tool-verified translation dramatically improves constraint satisfaction and preserves rhyme structure substantially better than a supervised baseline, while requiring no task-specific training and no parallel corpora, and transferring to Spanish and Japanese targets with only a small language-specific syllabification adapter.