In this study, bilayer electrospun scaffolds based on chitosan/polycaprolactone (CS/PCL) containing green-synthesized silver nanoparticles (AgNPs) were prepared and evaluated as novel wound dressings. The AgNPs were synthesized using a natural honey solution and silver nitrate, where the change in solution color and the emergence of an absorption peak at 405 nm confirmed successful formation. The synthesized nanoparticles exhibited a size range of 90–120 nm with acceptable uniform distribution. The electrospun scaffolds were fabricated with a PCL bottom layer and a CS-AgNP top layer, featuring a uniform structure with appropriate porosity and a mean fiber diameter of 50–100 nm. Swelling behavior analysis revealed that the scaffolds achieved a maximum swelling ratio of 420% and an equilibrium swelling of 300%. Silver release assays indicated that approximately 96% of the nanoparticles were released within 12 hours, followed by a quasi-stable release profile. The antioxidant activity, measured via DPPH assay, increased to 76% radical scavenging for the honey-AgNP formulation. Furthermore, antibacterial assays using the disk diffusion method demonstrated inhibition zones of 28 mm for Staphylococcus aureus and 22 mm for Escherichia coli, showing a significant increase compared to AgNP-free control samples. Overall, the synergy between CS, PCL, and honey-mediated AgNPs simultaneously improved antioxidant, antibacterial, and controlled-release properties, positioning this system as a promising candidate for smart wound dressings and the treatment of chronic infected wounds.