Accurate delineation of skin lesions in images is important for skin cancer detection. Existing methods often struggle with inherent complexities, such as irregular boundaries, textures, and artefacts in skin lesions. The study proposes a hybrid model comprising the edge-accurate LEDNet and Swin-UMamba for multiscale segmentation. The irregular boundaries and complex textures of skin lesions can be captured more effectively through this integration than with previous stand-alone methods. The structure of LEDNet includes components that enable it to segment lesions of various types effectively. Swin-Mamba is an encoder that uses Mamba-based architecture with the additional component of the VSS block. The proposed model is evaluated on the Ph, ISIC-2017 and ISIC-2018 skin cancer datasets and demonstrates robust performance across all datasets. The method achieved a Dice Similarity Coefficient (DSC) of 0.9734, a sensitivity of 0.9697, a specificity of 0.9858 and an accuracy of 0.9847 with ISIC 2017, DSC of 0.9753, a sensitivity of 0.9494, a specificity of 0.9902 and an accuracy of 0.9713 with ISIC 2018; and a DSC of 0.9801, a sensitivity of 0.9892, a specificity of 0.9966 and an accuracy of 0.9932 with Ph. These results show that the proposed hybrid framework has the potential to bring important benefits in the segmentation of skin lesions and is promising in clinical dermatology.