Autonomous Underwater Vehicles (AUVs) encounter significant energy, control and navigation challenges in complex underwater environments, particularly during close-proximity operations, such as launch and recovery (LAR), where fluid interactions and wake effects present additional navigational and energy challenges. Traditional path planning methods fail to incorporate these detailed wake structures, resulting in increased energy consumption, reduced control stability, and heightened safety risks. This paper presents a novel wake-informed, 3D path planning approach that fully integrates localized wake effects and global currents into the planning algorithm. Two variants of the A* algorithm - a current-informed planner and a wake-informed planner - are created to assess its validity and two neural network models are then trained to approximate these planners for real-time applications. Both the A* planners and NN models are evaluated using important metrics such as energy expenditure, path length, and encounters with high-velocity and turbulent regions. The results demonstrate a wake-informed A* planner consistently achieves the lowest energy expenditure and minimizes encounters with high-velocity regions, reducing energy consumption by up to 11.3%. The neural network models are observed to offer computational speedup of 6 orders of magnitude, but exhibit 4.51 - 19.79% higher energy expenditures and 9.81 - 24.38% less optimal paths. These findings underscore the importance of incorporating detailed wake structures into traditional path planning algorithms and the benefits of neural network approximations to enhance energy efficiency and operational safety for AUVs in complex 3D domains.