Early and reliable detection of heart murmurs is essential for the timely diagnosis of cardiovascular diseases, yet traditional auscultation remains subjective and dependent on expert interpretation. This work investigates artificial intelligence (AI)-based murmur detection using the CirCor Heart Sound dataset, with a focus on enabling uncertainty-aware, resource-efficient deployment on edge devices. Three convolutional neural network (CNN) architectures of increasing complexity (Light, Baseline, and Heavy) were compared in terms of classification performance, computational cost, and suitability for on-device inference. Additionally, Monte Carlo Dropout was applied for uncertainty estimation, providing confidence measures to improve prediction sensitivity. Results show that lightweight models can achieve accuracy comparable to deeper networks (91%) while requiring two orders of magnitude fewer parameters. Incorporating uncertainty-based selective classification further improved sensitivity by 3%, enhancing robustness and clinical reliability. The findings highlight the feasibility of developing computationally efficient, uncertainty-aware AI systems for heart murmur screening in low-resource and remote healthcare settings.