Developing a rapidly gel-forming, in situ sprayable hydrogel with wound dressing functionality is essential for enhancing the wound healing process. In this study, a novel sprayable hydrogel-based wound dressing was developed by combining thermo- and pH- responsive polymers including Pluronic F127 (PF127) and N-succinyl chitosan (NSC). NSC was prepared by modifying chitosan with succinic anhydride, as confirmed by Fourier-transform infrared spectroscopy and nuclear magnetic resonance spectroscopy. The NSC synthesized using a succinic anhydride-to-chitosan molar ratio of 5:1 exhibited the highest degree of substitution, resulting in a water-soluble polymer effective over a broad pH range. The formulation process of the PF127:NSC sprayable hydrogel was optimized and evaluated based on its sol–gel phase transition behavior, clarity, gelation time, liquid and moisture management, stability, and cytotoxicity. These properties can be suitably tailored by adjusting the concentrations of PF127 and NSC. Moreover, the antioxidant capacity of the hydrogels was enhanced by incorporating Azadirachta indica (neem) extract, a bioactive compound, into the optimized sprayable hydrogel. Both neem release and antioxidant activity increased in a dose-dependent manner. Overall, the developed sprayable hydrogel exhibited favorable sprayability, appropriate gelation properties, controlled drug release, and antioxidant activity, underscoring its promising translational potential as a wound dressing.