Skin cancer, particularly melanoma, is a serious dermatological condition that requires significant attention due to its potential severity. The remarkable progress in artificial intelligence (AI) in dermatology has brought diagnostic accuracies closer to those of human experts. However, clinical adoption remains hindered by transparency and interpretability gaps. In this paper, we propose a novel hybrid framework for automated melanoma detection that combines traditional machine learning (support vector machine, random forest), state-of-the-art convolutional neural networks (ResNet-152, MobileNet-V3), and transformer-based models (ViT-B16) with systematic post-hoc explainability analysis. We conduct detailed evaluations using the Grad-CAM and LayerCAM methods to assess visual trustworthiness and interpretability across different skin lesion types for clinical adoption. Our proposed framework, validated on two popular dermatology datasets (ISIC 2018 and 2019), demonstrates state-of-the-art performance (accuracy > 96%) for melanoma detection using ViTs-B16 and CNNs. Grad-CAM and LayerCAM visual explanations consistently align with dermatologist diagnostic criteria such as border irregularities, lesion area, and pigmentation asymmetries. This dual optimization of diagnostic accuracy and explainability bridges the critical gap between AI performance and clinical trust, thereby advancing the adoption of AI-driven tools in dermatological care.