Skin cancer is among the most prevalent and potentially deadly cancers worldwide, with early detection essential for effective treatment, particularly for aggressive types such as melanoma. Deep learning (DL) models have shown strong performance in skin lesion classification tasks, yet they often struggle to capture the complex geometric and topological structures present in dermoscopic images. In this study, we propose a hybrid classification framework that combines topological descriptors with CNNs and Vision Transformers to improve diagnostic performance across multiple categories of skin lesions. By extracting topological signatures, we quantify shape and connectivity patterns that are often overlooked by standard convolutional neural networks. Our experiments in multiple publicly available dermatology datasets demonstrate that topological models perform competitively on their own, and their integration with DL models consistently improves classification metrics. These results establish topological features as a valuable complement to deep learning in the diagnosis of skin cancer.