Electrospun nanocomposite polymer blend poly(vinylidene difluoride-co-hexafluoropropylene) (PVDF-HFP)/poly(methyl methacrylate) (PMMA) membranes with a novel dispersion of x wt % of one-dimensional (1D) TiO2 nanofiber fillers (x = 0.0–0.8 in steps of 0.2) were developed using the electrospinning technique. The developed nanocomposite polymer membranes were activated using various redox agents such as LiI, NaI, KI, and tetrabutyl ammonium iodide (TBAI). Introduction of the 1D TiO2 nanofiber fillers improves the amorphous nature of the blended polymer membrane, as confirmed through X-ray diffraction (XRD) and Fourier transform infrared (FTIR), and yielded an electrolyte uptake of over 480% for a 6 wt % TiO2 nanofiber filler-dispersed sample. PVDF-HFP/PMMA–1D 6 wt % TiO2 nanofiber fillers with the LiI-based redox electrolyte provided a high conductivity of 2.80 × 10–2 S cm–1 and a power conversion efficiency (PCE) of 8.08% to their fabricated dye-sensitized solar cells (DSSCs). The observed better ionic conductivity and efficiency of the fabricated DSSCs could be due to the faster movement of the smaller-ionic-radius (Li) ions entrapped inside the amorphous polymer. This enhanced mobility of ions in the quasi-solid electrolyte leads to faster regeneration of the depleting electrons in the photoanode, resulting in improved efficiency. Further, the achieved high conductivity was analyzed in terms of the dynamics and relaxation mechanisms involved by the ionic charge carriers with complex impedance spectroscopy using a random barrier model and Havriliak–Negami formulation. It was observed that the high-conducting PVDF-HFP/PMMA–1D 6 wt % TiO2 nanofiber fillers with LiI-based redox electrolyte show better ac conductivity parameters such as a σ of 5.82 × 10–2 S cm–1, ωe (12685 rad s–1), τe (0.909 × 10–4 s), and n (0.578). Also, dielectric studies revealed that the high-conducting sample has a higher dielectric constant and subsequently high loss. The J–V characteristics were studied using the equivalent circuit of a single-diode model, and the parameters influencing the photovoltaic performance were determined by Symbiotic Organisms Search (SOS) algorithm. The results suggest that the high-efficient sample possesses a minimum series resistance of 1.33 Ω and a maximum shunt resistance of 997 Ω. Hence, the highest-conducting electrospun-blended polymeric nanocomposite (PVDF-HFP–PMMA–6 wt % TiO2 nanofiber fillers) with LiI-based redox agent and tert-butyl pyridine (TBP) additive as the polymer quasi-solid electrolyte nanofibrous membrane can be a better electrolyte for high-performance dye-sensitized solar cell applications.