Skin cancer is among the most prevalent cancers globally, emphasizing the need for early detection and accurate diagnosis to improve outcomes. Traditional diagnostic methods, based on visual examination, are subjective, time-intensive, and require specialized expertise. Current artificial intelligence (AI) approaches for skin cancer detection face challenges such as computational inefficiency, lack of interpretability, and reliance on standalone CNN architectures. To address these limitations, this study proposes a comprehensive pipeline combining transfer learning, feature selection, and machine-learning algorithms to improve detection accuracy. Multiple pretrained CNN models were evaluated, with Xception emerging as the optimal choice for its balance of computational efficiency and performance. An ablation study further validated the effectiveness of freezing task-specific layers within the Xception architecture. Feature dimensionality was optimized using Particle Swarm Optimization, reducing dimensions from 1024 to 508, significantly enhancing computational efficiency. Machine-learning classifiers, including Subspace KNN and Medium Gaussian SVM, further improved classification accuracy. Evaluated on the ISIC 2018 and HAM10000 datasets, the proposed pipeline achieved impressive accuracies of 98.5% and 86.1%, respectively. Moreover, Explainable-AI (XAI) techniques, such as Grad-CAM, LIME, and Occlusion Sensitivity, enhanced interpretability. This approach provides a robust, efficient, and interpretable solution for automated skin cancer diagnosis in clinical applications.