(1) Background: Three-dimensional (3D) collagen I-based skin models are commonly used in drug development and substance testing but have major drawbacks such as batch-to-batch variations and ethical concerns. Recently, synthetic nanofibrous scaffolds created by electrospinning have received increasing interest as potential alternatives due to their morphological similarities to native collagen fibrils in size and orientation. The overall objective of this proof-of-concept study was to demonstrate the suitability of two synthetic polymers in creating electrospun scaffolds for 3D skin cell models. (2) Methods: Electrospun nanofiber mats were produced with (i) poly(acrylonitrile-co-methyl acrylate) (P(AN-MA)) and (ii) a blend of pullulan (Pul), poly(vinyl alcohol) (PVA) and poly(acrylic acid) (PAA) (Pul/PVA/PAA) and characterized by scanning electron microscopy (SEM) and diffuse reflectance infrared Fourier transform (DRIFT) spectra. Primary skin fibroblasts and keratinocytes were seeded onto the nanofiber mats and analyzed for phenotypic characteristics (phalloidin staining), viability (Presto Blue HS assay), proliferation (Ki-67 staining), distribution (H/E staining), responsiveness to biological stimuli (qPCR), and formation of skin-like structures (H/E staining). (3) Results: P(AN-MA) mats were more loosely packed than the Pul/PVA/PAA mats, concomitant with larger fiber diameter (340 nm ± 120 nm vs. 250 nm ± 120 nm, p < 0.0001). After sterilization and exposure to cell culture media for 28 days, P(AN-MA) mats showed significant adsorption of fetal calf serum (FCS) from the media into the fibers (DRIFT spectra) and increased fiber diameter (590 nm ± 290 nm, p < 0.0001). Skin fibroblasts were viable over time on both nanofiber mats, but suitable cell infiltration only occurred in the P(AN-MA) nanofiber mats. On P(AN-MA) mats, fibroblasts showed their characteristic spindle-like shape, produced a dermis-like structure, and responded well to TGFβ stimulation, with a significant increase in the mRNA expression of PAI1, COL1A1, and αSMA (all p < 0.05). Primary keratinocytes seeded on top of the dermis equivalent proliferated and formed a stratified epidermis-like structure. (4) Conclusion: P(AN-MA) and Pul/PVA/PAA are both biocompatible materials suitable for nanofiber mat production. P(AN-MA) mats hold greater potential as future 3D skin models due to enhanced cell compatibility (i.e., adsorption of FCS proteins), cell infiltration (i.e., increased pore size due to swelling behavior), and cell phenotype preservation. Thus, our proof-of-concept study shows an easy and robust process of producing electrospun scaffolds for 3D skin cell models made of P(AN-MA) nanofibers without the need for bioactive molecule attachments.