The rapid advancement of deep learning in medical image analysis has greatly enhanced the accuracy of skin cancer classification. However, current state-of-the-art models, especially those based on transfer learning like ResNet50, come with significant computational overhead, rendering them impractical for deployment in resource-constrained environments. This study proposes a custom CNN model that achieves a 96.7\% reduction in parameters (from 23.9 million in ResNet50 to 692,000) while maintaining a classification accuracy deviation of less than 0.022\%. Our empirical analysis of the HAM10000 dataset reveals that although transfer learning models provide a marginal accuracy improvement of approximately 0.022\%, they result in a staggering 13,216.76\% increase in FLOPs, considerably raising computational costs and inference latency. In contrast, our lightweight CNN architecture, which encompasses only 30.04 million FLOPs compared to ResNet50's 4.00 billion, significantly reduces energy consumption, memory footprint, and inference time. These findings underscore the trade-off between the complexity of deep models and their real-world feasibility, positioning our optimized CNN as a practical solution for mobile and edge-based skin cancer diagnostics.