Skin cancer is a common and potentially fatal disease where early detection is crucial, especially for melanoma. Current deep learning systems classify skin lesions well, but they primarily rely on appearance cues and may miss deeper structural patterns in lesions. We present TopoCon-MP, a method that extracts multiparameter topological signatures from dermoscopic images to capture multiscale lesion structure, and fuses these signatures with Vision Transformers using a supervised contrastive objective. Across three public datasets, TopoCon-MP improves in-distribution performance over strong pretrained CNN and ViT baselines, and in cross-dataset transfer, it maintains competitive performance. Ablations show that both multiparameter topology and contrastive fusion contribute to these gains. The resulting topological channels also provide an interpretable view of lesion organization that aligns with clinically meaningful structures. Overall, TopoCon-MP demonstrates that multipersistence-based topology can serve as a complementary modality for more robust skin cancer detection.