Composite nanofibrous yarns (CNY), featuring a submicron electrospun sheath coated on a micro-scale core yarn have gained attention within the academic and industrial communities due to their unique structure. When braided, these CNYs hold great promise as next-generation surgical yarns. However, large-scale production of CNYs using conventional electrospinning techniques remains technologically challenging, and maintaining the integrity of the fibrous sheath during braiding presents further difficulties. Here, we propose a novel approach for continuously fabricating functional braided CNYs using collectorless alternating current (AC) electrospinning and braiding technology. Our approach utilized polycaprolactone-polylactic acid (PCL-PLA) blends and PCL-PLA with chlorhexidine (CHX) or triclosan (TRC) electrospun fibers for the sheath layer, while PLA micro-yarns acted as the core layer. Morphological analyses confirmed the successful fabrication of braided CNYs. Additionally, infrared spectroscopy validated the presence of CHX or TRC in the resulting yarns. The resulting braided CNYs exhibited excellent breaking force (29 N) and thermal stability (270 °C). Cytotoxicity and antibacterial assessments demonstrated that CHX-loaded braided CNYs could serve as biocompatible antibacterial surgical sutures. The proposed method offers a versatile approach for producing various functional braided CNYs applicable in tissue engineering scaffolds, filters, wearable electronics, and sensors.