Skin cancer is a rather widespread and potentially dangerous disease with aggressive malignancies that make fast metastasis in case of belated diagnosis. In turn, early detection of the disease significantly increases the chances of successful treatment and thus a favorable prognosis; therefore, diagnostic techniques need to be developed that possess both high sensitivity and specificity. The approach used in this paper employed the transfer learning skin cancer detection with advanced CNN techniques for classifying skin lesions as malignant or benign to enable early detection. The current study, therefore, focuses on the transfer learning methodology based on MobileNet architecture and has presented great potential regarding accuracy in malignancy detection. The next section presents a baseline comparison by proposing a custom CNN model for skin cancer classification, named DermCNN. Finally, we propose AccuDermCNN, a custom CNN model enhanced with edge detection techniques to further improve detection accuracy. Comparative analyses will demonstrate that all models, including AccuDermCNN, are on par with state-of-the-art methods and thus provide reliable diagnostic support. The results highlight that the integration of advanced CNN architectures, especially transfer learning and edge detection, can be effectively used for the medical diagnosis of skin cancer.