Shape memory polymers (SMPs) represent a class of smart materials of increasing importance in biomaterials engineering and dermatological applications. Their ability to undergo reversible shape changes in response to physiological stimuli enables the design of materials capable of conforming to the skin surface and enhancing the performance of delivery systems. The aim of this study was to evaluate the effect of zinc oxide (ZnO) addition on the electrospinning process and the properties of electrospun fibrous mats based on a poly(L-lactide-co-glycolide-co-caprolactone) (PLGC) exhibiting shape memory behavior. The fibrous mats were fabricated by electrospinning using a chloroform/methanol solvent system (1:1 v/v). It was demonstrated that ZnO content significantly influences the morphology of the material — at 0.5 wt% a fibrous structure was obtained, whereas higher concentrations (2.5 and 5 wt%) resulted in the loss of fibrous morphology and the formation of more compact structures. FTIR analysis confirmed the presence of ZnO without significant changes in the chemical structure of the polymer. All samples retained shape memory properties at a temperature close to human body temperature, indicating their potential applicability under physiological conditions. The obtained results demonstrate that ZnO content governs the morphology transition from fibrous mats to compact film-like structures, which in turn significantly affects shape memory behavior; low ZnO concentrations favor the formation of uniform fibrous materials suitable for skin-related applications, whereas higher concentrations lead to dense, film-like structures that may serve as protective or occlusive layers, while still retaining functional shape memory properties.