Skin cancer classification is a crucial task in medical image analysis, where precise differentiation between malignant and non-malignant lesions is essential for early diagnosis and treatment. In this study, we explore Sequential and Parallel Hybrid CNN-Transformer models with Convolutional Kolmogorov-Arnold Network (CKAN). Our approach integrates transfer learning and extensive data augmentation, where CNNs extract local spatial features, Transformers model global dependencies, and CKAN facilitates nonlinear feature fusion for improved representation learning. To assess generalization, we evaluate our models on multiple benchmark datasets (HAM10000,BCN20000 and PAD-UFES) under varying data distributions and class imbalances. Experimental results demonstrate that hybrid CNN-Transformer architectures effectively capture both spatial and contextual features, leading to improved classification performance. Additionally, the integration of CKAN enhances feature fusion through learnable activation functions, yielding more discriminative representations. Our proposed approach achieves competitive performance in skin cancer classification, demonstrating 92.81% accuracy and 92.47% F1-score on the HAM10000 dataset, 97.83% accuracy and 97.83% F1-score on the PAD-UFES dataset, and 91.17% accuracy with 91.79% F1- score on the BCN20000 dataset highlighting the effectiveness and generalizability of our model across diverse datasets. This study highlights the significance of feature representation and model design in advancing robust and accurate medical image classification.