The complex feature characteristics and low contrast of cancer lesions, a high degree of inter-class resemblance between malignant and benign lesions, and the presence of various artifacts including hairs make automated melanoma recognition in dermoscopy images quite challenging. To date, various computer-aided solutions have been proposed to identify and classify skin cancer. In this paper, a deep learning model with a shallow architecture is proposed to classify the lesions into benign and malignant. To achieve effective training while limiting overfitting problems due to limited training data, image preprocessing and data augmentation processes are introduced. After this, the 'box blur' down-scaling method is employed, which adds efficiency to our study by reducing the overall training time and space complexity significantly. Our proposed shallow convolutional neural network (SCNN_12) model is trained and evaluated on the Kaggle skin cancer data ISIC archive which was augmented to 16485 images by implementing different augmentation techniques. The model was able to achieve an accuracy of 98.87% with optimizer Adam and a learning rate of 0.001. In this regard, parameter and hyper-parameters of the model are determined by performing ablation studies. To assert no occurrence of overfitting, experiments are carried out exploring k-fold cross-validation and different dataset split ratios. Furthermore, to affirm the robustness the model is evaluated on noisy data to examine the performance when the image quality gets corrupted.This research corroborates that effective training for medical image analysis, addressing training time and space complexity, is possible even with a lightweighted network using a limited amount of training data.