The COVID-19 pandemic has underscored the need for accessible and efficient screening methods. This study proposes a hybrid handcrafted and deep transfer learning-based framework for COVID-19 detection using voice analysis. The approach combines handcrafted non-cepstral acoustic features, such as jitter, shimmer, and fundamental frequency, with high-dimensional embeddings extracted from a pre-trained deep learning voice-to-vector model. This fusion enables a comprehensive feature representation, capturing both handcrafted signal-based attributes and deep spectral representations. Various supervised classifiers, including Random Forest, CatBoost, and XGBoost, are trained and optimized using data balancing strategies and hyperparameter tuning techniques. Experimental results demonstrate that the proposed hybrid framework effectively differentiates between COVID-19 positive and negative individuals, achieving competitive performance compared to existing studies. These findings reinforce the potential of voice-based COVID-19 detection as a scalable, non-invasive, and cost-effective screening tool.