Natural polymer-based nanoparticles have emerged as promising stabilizers for Pickering emulsions, offering biocompatibility, environmental sustainability, and improved protection of active compounds. This study developed chitosan/gum arabic (CH/GA) nanoparticles as solid stabilizers for quercetin-loaded Pickering emulsions to enhance the stability and antioxidant bioactivity of quercetin (QE), a plant-derived flavonoid known for its potent radical-scavenging activity but limited by oxidative degradation. A systematic formulation strategy was employed to evaluate the effects of CH/GA concentration (0.5–2.0% w/v), oil type (olive, soybean, sunflower, and coconut), and oil volume fraction (ϕ = 0.5–0.7) on emulsion stability. The formulation containing 1.5% CH/GA and olive oil at ϕ = 0.6 exhibited optimal physical and interfacial stability. Quercetin (0.1% w/w) was incorporated into the optimized emulsions and characterized for long-term stability, particle size, droplet morphology, rheology, antioxidant activity (DPPH), cytocompatibility, and intracellular reactive oxygen species (ROS) protection using HaCaT keratinocytes. The olive oil-based formulation (D1-QE) exhibited greater viscosity retention and antioxidant stability than its soybean-based counterpart (E2-QE) under both room temperature (RT) and accelerated heating–cooling (H/C) storage conditions. Confocal microscopy confirmed the accumulation of CH/GA nanoparticles at the oil–water interface, forming a dense interfacial barrier and enhancing emulsion stability. HPLC analysis showed that D1-QE retained 92.8 ± 0.5% of QE at RT and 82.8 ± 1.5% under H/C conditions after 30 days. Antioxidant activity was largely preserved, with only 4.7 ± 1.7% and 14.9 ± 4.8% loss of DPPH radical scavenging activity at RT and H/C, respectively. Cytotoxicity testing in HaCaT keratinocytes confirmed that the emulsions were non-toxic at 1 mg/mL QE and effectively reduced H₂O₂-induced oxidative stress, decreasing intracellular ROS levels by 75.16%. These results highlight the potential of CH/GA-stabilized Pickering emulsions as a polymer-based delivery system for maintaining the stability and functional antioxidant activity of QE in bioactive formulations.