In chronic wound (CW) scenarios, Staphylococcus aureus-induced infections are very prevalent. This leads to abnormal inflammatory processes, in which proteolytic enzymes, such as human neutrophil elastase (HNE), become highly expressed. Alanine-Alanine-Proline-Valine (AAPV) is an antimicrobial tetrapeptide capable of suppressing the HNE activity, restoring its expression to standard rates. Here, we proposed the incorporation of the peptide AAPV within an innovative co-axial drug delivery system, in which the peptide liberation was controlled by N-carboxymethyl chitosan (NCMC) solubilization, a pH-sensitive antimicrobial polymer effective against Staphylococcus aureus. The microfibers' core was composed of polycaprolactone (PCL), a mechanically resilient polymer, and AAPV, while the shell was made of the highly hydrated and absorbent sodium alginate (SA) and NCMC, responsive to neutral-basic pH (characteristic of CW). NCMC was loaded at twice its minimum bactericidal concentration (6.144 mg/mL) against S. aureus, while AAPV was loaded at its maximum inhibitory concentration against HNE (50 μg/mL), and the production of fibers with a core-shell structure, in which all components could be detected (directly or indirectly), was confirmed. Core-shell fibers were characterized as flexible and mechanically resilient, and structurally stable after 28-days of immersion in physiological-like environments. Time-kill kinetics evaluations revealed the effective action of NCMC against S. aureus, while elastase inhibitory activity examinations proved the ability of AAPV to reduce HNE levels. Cell biology testing confirmed the safety of the engineered fiber system for human tissue contact, with fibroblast-like cells and human keratinocytes maintaining their morphology while in contact with the produced fibers. Data confirmed the engineered drug delivery platform as potentially effective for applications in CW care.