Dermoscopic skin lesion classification is a task of major clinical importance but is computationally expensive, making it inaccessible in resource-constrained healthcare settings. In this paper, we introduce a computationally efficient skin lesion classification framework for seven classes using EfficientNet-B0, complemented by Monte Carlo (MC) Dropout for uncertainty quantification. Our approach was trained and tested on the HAM10000 dataset containing 10,015 dermoscopic images across seven classes. To address the severe 67:1 class imbalance, we employ WeightedRandomSamplerand class-weighted cross-entropy loss as complementary corrections acting at the batch-composition level and the gradient-magnitude level respectively. By performing $T=50$ stochastic forward passes during inference, we decompose predictive uncertainty into aleatoric and epistemic components and apply an entropy-based referral threshold that flags uncertain predictions for specialist review. To validate spatial interpretability, Gradient-weighted Class Activation Mapping (Grad-CAM) is applied and quantitatively evaluated via Intersection over Union (IoU) against ISIC segmentation masks, yielding a mean IoU of 0.61 across all accepted predictions. Our experiments achieve a test macro AUROC of 0.9404and macro F1-score of 0.7308, with six of seven classes exceeding 70% per-class accuracy (melanocytic nevi: 69.8%). Referring the 30% most uncertain predictions to a clinician raises accepted-subset AUROC from 0.9404 to 0.9568 ($+1.64\%$). The framework is competitive with ResNet-50 and DenseNet-121 at one-fifth the parameter count, and the only lightweight method in the comparison providing calibrated uncertainty estimates. Inference latency benchmarks on an NVIDIA Jetson Nano (edge CPU mode) are reported to contextualize deployment feasibility.