Early and reliable identification of cardiac disorders from Phonocardiogram (PCG) signals acquired from wearable biosensors is critical to support clinical decision making and reduce subjectivity in auscultation-based assessments. This study proposes a multi-stage hybrid feature selection-classification approach to increase diagnostic accuracy without requiring computationally expensive deep learning (DL) architectures. First, the most statistically discriminative features were identified using mRMR, ReliefF, and Kruskal-Wallis filtering methods. Particle swarm optimization (PSO) and ant colony optimization (ACO) were then applied to optimize the solution space. Finally, the selected feature subsets were tested with k-nearest neighbor (k-NN), support vector machines (SVMs), and Bagged Tree (BT) classifiers. Experimental results show that the proposed method significantly increases the model robustness and generalizability. In particular, the Kruskal-Wallis+k-NN and ReliefF+k-NN combinations achieved competitive performance compared to many DL-based approaches in the literature, with 99.80% accuracy and 99.50% F1-score. Furthermore, hybrid models augmented with PSO and ACO also achieved 99.60% accuracy. The findings demonstrate that well-designed feature selection strategies offer high accuracy and enhanced clinical applicability while using only a small set of handcrafted features and conventional classifiers. Therefore, the proposed framework is a strong candidate for smart stethoscope-based early screening solutions.