This research introduces a novel hybrid deep learning framework integrating Big Transfer Learning (BiT M-R50x1) and EfficientNet B6 to automate the detection of skin cancer and monkeypox (Mpox) from dermatoscopic images. By using BiT's powerful knowledge transfer from large-scale datasets and EfficientNet’s computational efficiency, the system achieves superior classification accuracy while maintaining inference speed—critical for deployment in resource-limited clinical settings. The framework employs comprehensive preprocessing, including resizing, normalization, and targeted augmentation, to address class imbalance across benign, malignant, and Mpox lesion images. It utilizes ISIC-2020 and Kaggle Mpox datasets for training and evaluation. The hybrid model’s architecture freezes base layers to retain generic image features while fine-tuning the top layers for task-specific learning. The system achieves an accuracy of 95.5%, precision of 94%, recall of 91.69%, and an F1-score of 93.36%, outperforming baseline models like InceptionV3, ResNet50, and MobileNetV2. Experimental results confirm robust classification performance even with limited annotated data for rare diseases like Mpox. Additionally, demographic-based evaluation revealed strong consistency across gender and age subgroups, with slightly higher sensitivity in older patients. This work demonstrates the efficacy of hybrid AI models in delivering fast, reliable, and interpretable diagnostics, with significant potential for real-world deployment in dermatological and infectious disease screening.