This work assesses the hydrodynamic efficiency of Underwater Unmanned Vehicles (UUVs) equipped with soft morphing wings compared to conventional rigid wings. Unlike rigid wings, deformable counterparts can alter their aerodynamic properties on demand. Improvements in hydrodynamic efficiency extend a UUV's operational range and may determine mission feasibility. Structural and Computational Fluid Dynamics (CFD) simulations were conducted for both a soft morphing wing and a UUV incorporating it. The results show that a UUV employing soft wings achieves 9.75 percent higher overall efficiency than an equivalent vehicle with traditional rigid wings. These findings confirm the potential of soft robotics to enhance underwater vehicle performance, particularly in applications requiring pressure-agnostic operation.