Monkeypox (MPox) has emerged as a significant global concern, with cases steadily increasing daily. Conventional detection methods, including polymerase chain reaction (PCR) and manual examination, exhibit challenges of low sensitivity, high cost, and substantial workload. Therefore, deep learning offers an automated solution; however, the datasets include data scarcity, texture, contrast, inter-intra class variability, and similarities with other skin infectious diseases. In this regard, a novel hybrid approach is proposed that integrates the learning capacity of Residual Learning and Spatial Exploitation Convolutional Neural Network (CNN) with a customized Swin Transformer (RS-FME-SwinT) to capture multi-scale global and local correlated features for MPox diagnosis. The proposed RS-FME-SwinT technique employs a transfer learning-based feature map enhancement (FME) technique, integrating the customized SwinT for global information capture, residual blocks for texture extraction, and spatial blocks for local contrast variations. Moreover, incorporating new inverse residual blocks within the proposed SwinT effectively captures local patterns and mitigates vanishing gradients. The proposed RS-FME-SwinT has strong learning potential of diverse features that systematically reduce intra-class MPox variation and enable precise discrimination from other skin diseases. Finally, the proposed RS-FME-SwinT is a holdout cross-validated on a diverse MPox dataset and achieved outperformance on state-of-the-art CNNs and ViTs. The proposed RS-FME-SwinT demonstrates commendable results of an accuracy of 97.80%, sensitivity of 96.82%, precision of 98.06%, and an F-score of 97.44% in MPox detection. The RS-FME-SwinT could be a valuable tool for healthcare practitioners, enabling prompt and accurate MPox diagnosis and contributing significantly to mitigation efforts.