Skin cancer is one of the leading types of cancer in the world, affecting a large part of the population globally. There is a need to develop a precise classification technique to detect benign and malignant tumors non-invasively from dermoscopic images. This paper proposes a novel lightweight deep learning model, Multiscale-FocusNet, for improved diagnosis of skin cancer. This work integrates advanced preprocessing and color consistency techniques with a novel dual attention model built on modified MobileNet-V2 architecture. The proposed method is validated on the public ISIC Challenge dataset. The proposed Multiscale-FocusNet exhibits exceptional performance, achieving 98.85% accuracy, 99.28% precision, 98.21% recall, and 98.74% F1-score. The Multiscale-FocusNet shows a superior promising performance as compared to existing transfer learning models. The proposed method can be effectively used for precise detection of skin cancer using dermoscopic images.