The study focuses on the fabrication and characterization of ciprofloxacin (CIP)/paclitaxel (PTX)-loaded pullulan/poly(lactic-co-glycolic acid) (PLGA) core/sheath nanofibers using the highly efficient coaxial electrocentrifugal spinning (ECS) technique. In contrast to conventional coaxial electrospinning, the in-house developed coaxial ECS setup used in this study effectively tackled the nozzle cleaning issue. In this study, core/sheath nanofibers with varying core-to-sheath ratio were fabricated, demonstrating suitable mechanical properties for use in biomedical applications. The primary objective was to determine the effect of core-to-sheath ratio on mechanical properties and dual drug release kinetics of the nanofibers. Additionally, the in vitro drug release study demonstrated simultaneous release profiles of CIP from the core and PTX from the sheath. The nanofibers exhibited initial burst release of 6 h, followed by controlled release, making them suitable for targeted therapeutic applications. Moreover, the in vitro cytotoxicity analysis demonstrated enhanced cytotoxic efficacy of the combination of CIP and PTX toward human melanoma A375 cells. The dual drug-loaded 23G/1 mm and 21G/1 mm nanofibers demonstrated 65.37% ± 1.96% and 67.82% ± 1.31% melanoma cell viability after 72 h, indicating significant cytotoxicity. This further highlights the possible potentiality of the nanofibers toward melanoma treatment and their application as dual drug delivery systems with tunable drug release properties.