The most deadly type of skin cancer is melanoma. A visual examination does not provide an accurate diagnosis of melanoma during its early to middle stages. Therefore, an automated model could be developed that assists with early skin cancer detection. It is possible to limit the severity of melanoma by detecting it early and treating it promptly. This study aims to develop efficient approaches for various phases of melanoma computer-aided diagnosis (CAD), such as preprocessing, segmentation, and classification. The first step of the CAD pipeline includes the proposed hybrid method, which uses morphological operations and context aggregation-based deep neural networks to remove hairlines and improve poor contrast in dermoscopic skin cancer images. An image segmentation network based on deep learning is then used to extract lesion regions for detailed analysis and calculate the optimized classification features. Lastly, a deep neural network is used to distinguish melanoma from benign lesions. The proposed approaches use a benchmark dataset named International Skin Imaging Collaboration (ISIC) 2020. In this work, two forms of evaluations are performed with the classification model. The first experiment involves the incorporation of the results from the preprocessing and segmentation stages into the classification model. The second experiment involves the evaluation of the classifier without employing these stages i.e., using raw images. From the study results, it can be concluded that a classification model using segmented and cleaned images contributes more to achieving an accurate classification rate of 93.40% with a 1.3 s test time on a single image.