Skin lesion classification is a critical task in dermatology, which requires accurate and efficient methods for early detection and diagnosis of skin conditions. In this study, we leverage transfer learning techniques to identify a lightweight pre-trained model among a pool of available pre-trained models for skin lesion classification for deployment on mobile devices. To identify such model, we evaluate and compare six pre-trained models under two distinct strategies: (i) Changing the last layer for a given number of classes and freezing weights of initial layers while learning weights involved in the last two layers and (ii) utilizing them as feature extractors in conjunction with traditional classifiers such as Support Vector Machine, Discriminant analysis, and Decision tree. The performance of these models is evaluated and compared on the ISIC 2018 dataset in terms of microF1_score, microSpecificity, AUC, memory requirement, and number of parameters of the model. Based on the ranking method, Shufflenet outperformed all other pre-trained models for skin lesion classification.