In this paper, we propose a multi-stage electrocardiogram (ECG) classifier for distributed machine learning (ML) inferencing across the edge-cloud continuum for wearable systems. Traditionally, biomedical data acquired from wearable systems are processed in one step, using a single-stage classifier deployed either on a cloud or on an edge device. Though there are merits, both approaches have limitations that relate to computational complexity, network connectivity, etc. In this work, we propose a multi-stage, cascaded, ensemble classifier that aims to address these limitations by decentralizing the processing steps, while achieving good overall performance. We employed low-complexity, explainable boosting machines (EBM) and convolutional neural networks (CNN) to develop a multi-stage distributed ECG classifier, which achieves a high-sensitivity binary classification on the edge device and a more comprehensive multi-class classification on the cloud. In standalone performance evaluation using the MIT-BIH Arrhythmia database, the Stage-1 EBM classifier and Stage-2 CNN classifier achieved a maximum accuracy, sensitivity of 96.71%, 96.76%, and 99.49%, 98.19% respectively. Further, the distributed multi-stage classifier achieved a maximum cumulative binary classification accuracy, sensitivity of 99.64%, 99.01%, and multi-class classification accuracy, sensitivity of 99.56%, 98.79% when DtC equals 40%. Further, we evaluated the use of the EBM classifier threshold as a control parameter to dynamically vary the system performance and network traffic based on real-time conditions. We verified the feasibility of the model, calculated the energy consumption, and estimated the latency. When streaming only 40% of the data to the cloud, it will result in 60% latency saving. With the proposed technique, energy consumption is reduced by approximately 3 times.