Breast cancer is a leading cause of death among women worldwide, emphasizing the need for early detection and accurate diagnosis. As such Ultrasound Imaging, a reliable and cost-effective tool, is used for this purpose, however the sensitive nature of medical data makes it challenging to develop accurate and private artificial intelligence models. A solution is Federated Learning as it is a promising technique for distributed machine learning on sensitive medical data while preserving patient privacy. However, training on non-Independent and non-Identically Distributed (non-IID) local datasets can impact the accuracy and generalization of the trained model, which is crucial for accurate tumour boundary delineation in BC segmentation. This study aims to tackle this challenge by applying the Federated Proximal (FedProx) method to non-IID Ultrasonic Breast Cancer Imaging datasets. Moreover, we focus on enhancing tumour segmentation accuracy by incorporating a modified U-Net model with attention mechanisms. Our approach resulted in a global model with 96% accuracy, demonstrating the effectiveness of our method in enhancing tumour segmentation accuracy while preserving patient privacy. Our findings suggest that FedProx has the potential to be a promising approach for training precise machine learning models on non-IID local medical datasets.