Human stress is intricately linked with mental processes such as decision making. Public protection practitioners, including Law Enforcement Agents (LEAs), are forced to make difficult decisions during high-pressure operations, under strenuous circumstances. In this respect, systems and applications that assist such practitioners to take decisions, are increasingly incorporating user stress level information for their development, adaptation, and evaluation. To that end, our goal is to accurately detect and classify the level of acute, short-term stress, in real time, for the development of personalized, context-aware solutions for LEAs. Deep Neural Networks (DNNs), and in particular Convolutional Neural Networks (CNNs), have been gaining traction in the field of stress analysis, exhibiting promising results. Furthermore, the electrocardiogram (ECG) signals, have also been widely adopted for estimating levels of stress. In this work, we propose two CNN architectures for the stress detection and 3-level (low, moderate, high) stress classification tasks, using ultra short-term raw ECG signals (3 s). One architecture is simple and with a low memory footprint, suitable for running in wearable edge-computing nodes, and the other is able to learn more complex features, having more trainable parameters. The models were trained on the two publicly available stress classification datasets, after applying pre-processing techniques, such as data pruning, down-sampling, and data augmentation, using a sliding window approach. After hyperparameter tuning, using 4-fold cross-validation, the evaluation on the test set demonstrated state-of-the-art accuracy both on the 3- and 2-level stress classification task using the DriveDB dataset, reporting an accuracy of 83.55% and 98.77% respectively.