This paper presents a comprehensive evaluation of deep learning (DL)-based skin lesion classification with transfer learning and uncertainty quantification (UQ) using the HAM10000 dataset. We benchmarked several pre-trained feature extractors, including CLIP variants, ResNet50, DenseNet121, VGG16, and EfficientNet-V2-Large, combined with traditional classifiers such as SVM, XGBoost, and logistic regression. We explored various PCA settings (64, 128, 256, and 512), and achieved the best baseline performance when LAION CLIP ViT-H/14 and ViT-L/14 were used with PCA-256. In the UQ step, we applied Monte Carlo Dropout (MCD), Ensemble, and Ensemble Monte Carlo Dropout (EMCD) and evaluated using uncertainty-aware metrics (UAcc, USen, USpe, and UPre). An ensemble method using PCA-256 provided the best balance between accuracy and reliability. Further improvements were achieved through feature fusion of the best-performing extractors. Finally, a feature fusion-based model trained with the predictive entropy (PE) loss function was proposed, achieving superior performance to all previous configurations in both standard and uncertainty-aware evaluations, thereby advancing reliable DL-based skin cancer diagnosis.