Skin diseases in melanin-rich skin often present diagnostic challenges due to the unique characteristics of darker skin tones, which can lead to misdiagnosis or delayed treatment. This disparity impacts millions within diverse communities, highlighting the need for accurate, AI-based diagnostic tools. In this paper, we investigated the performance of three machine learning methods -Support Vector Machines (SVMs), Random Forest (RF), and Decision Trees (DTs)-combined with state-of-the-art (SOTA) deep learning models, EfficientNet, MobileNetV2, and DenseNet121, for predicting skin conditions using dermoscopic images from the HAM10000 dataset. The features were extracted using the deep learning models, with the labels encoded numerically. To address the data imbalance, SMOTE and resampling techniques were applied. Additionally, Principal Component Analysis (PCA) was used for feature reduction, and fine-tuning was performed to optimize the models. The results demonstrated that RF with DenseNet121 achieved a superior accuracy of 98.32%, followed by SVM with MobileNetV2 at 98.08%, and Decision Tree with MobileNetV2 at 85.39%. The proposed methods overcome the SVM with the SOTA EfficientNet model, validating the robustness of the proposed approaches. Evaluation metrics such as accuracy, precision, recall, and F1-score were used to benchmark performance, showcasing the potential of these methods in advancing skin disease diagnostics for diverse populations.