Skin cancer (SC) comprises approximately 33% of all reported cancer cases globally. Thus, rapid and accurate diagnosis is crucial for effective treatment and better patient outcomes. Computer-aided diagnostic (CAD) systems are necessary for assisting and improving traditional diagnostic approaches, however, most of them count on only spatial information and/or individual deep-learning models to realize a diagnosis. Furthermore, current CADs retrieve deep features with substantial sizes, resulting in increased training complexity and speed. This article presents a CAD framework to classify multiple subcategories of SC based on multiple Convolutional Neural Networks (CNNs) with distinct configurations. The study explores various combinations of CNNs to select the best mixture of CNNs that impact performance. Additionally, it incorporates spatial and time-frequency demonstrations to successfully diagnose SC through the utilisation of wavelet analysis. In addition, wavelet analysis is employed to reduce the large dimensionality of deep features, which is further minimised using principal component analysis. The results indicate that the suggested CAD accomplished a rate of accuracy of 0.956 using only 159 features. It surpasses the CADs currently available. Therefore, it can serve as a powerful tool for identifying SC and could be employed to enhance the precision of medical diagnostics.