Chronic wounds (CWs) are a significant public health concern and affect 1-2% of the world's population. They are responsible for high morbidity and mortality rates. Bacterial infections caused by Staphylococcus aureus and Pseudomonas aeruginosa are very common in CWs and prevent normal wound healing steps from taking place. Carbon nanofibers (CNFs) have attracted interest due to their inherent antibacterial and blood clotting abilities, as well as mechanical strength. The aim of this research was to engineer coaxial fibers by wet-spinning as new platforms for drug delivery in CW care (promoting rapid blood clotting and consequent tissue regeneration). Coaxial fibers were produced with an outer layer (shell) made of a mechanically resilient polycaprolactone (PCL at 10 wt%) reinforced with carbon nanofibers (CNFs at 50, 100, and 150 μg mL-1), while the inner layer (core) was made of a highly hydrated mixture of 2 wt% sodium alginate (SA) loaded with ceftazidime (CZ) at 128 μg mL-1 (minimum bactericidal concentration). The fibers' double-layer structure was verified by scanning electron microscopy. Core-shell fibers were deemed highly flexible and mechanically resilient and resistant to rupture, with such properties being improved with the incorporation of CNFs. Most fibers preserved their structural integrity after 28 days of incubation in physiological-like medium. Furthermore, data reported the ability of CZ combined with CNFs to fight microbial proliferation and showed that the presence of CNFs promoted blood clotting, with PCL/CNFs50 being the most effective from the group. It was found that higher concentrations of CNFs had a detrimental effect, highlighting a concentration-dependent response. The presence of PLC in the fibers resulted in a mitigation of the CNFs' cytotoxic impact on keratinocytes. The incorporation of CZ had no effect on the metabolic activity of the cells. Overall, the results demonstrated the potentialities of the engineered coaxial fibers for applications in wound care.