Early detection of melanoma is crucial for improving survival rates. Current detection tools often utilize data-driven machine learning methods but often overlook the full integration of multiple datasets. We combine publicly available datasets to enhance data diversity, allowing numerous experiments to train and evaluate various classifiers. We then calibrate them to minimize misdiagnoses by incorporating uncertainty quantification. Our experiments on benchmark datasets show accuracies of up to 93.2% before and 97.8% after applying uncertainty-based rejection, leading to a reduction in misdiagnoses by over 40.5%. Our code and data are publicly available, and a web-based interface for quick melanoma detection of user-supplied images is also provided.