Dialogue Topic Segmentation (DTS) is crucial for understanding task-oriented public-channel communications, such as maritime VHF dialogues, which feature informal speech and implicit transitions. To address the limitations of traditional methods, we propose DASH-DTS, a novel LLM-based framework. Its core contributions are: (1) topic shift detection via dialogue handshake recognition; (2) contextual enhancement through similarity-guided example selection; and (3) the generation of selective positive and negative samples to improve model discrimination and robustness. Additionally, we release VHF-Dial, the first public dataset of real-world maritime VHF communications, to advance research in this domain. DASH-DTS provides interpretable reasoning and confidence scores for each segment. Experimental results demonstrate that our framework achieves several sota segmentation trusted accuracy on both VHF-Dial and standard benchmarks, establishing a strong foundation for stable monitoring and decision support in operational dialogues.