This paper introduces an innovative path planning strategy tailored to Unmanned Aerial Manipulation (UAM) systems for pick-and-place applications. It offers a solution for effectively coordinating the aerial platform with the manipulator robot to navigate around obstacles. This is achieved by establishing two distinct paths, one for the aerial platform and another for the manipulator robot, ensuring seamless operation and preventing collisions within the entire system. The core of this approach relies heavily on the novel Random Geometric Model (RGM) to position the aerial platform close to the target object, thus confirming that the object is within reach of its end-effector. It employs sampling-based methods and geometric models to efficiently explore the configuration space and generate collision-free path. The fundamental concept underlying this approach is to randomly generate points within the workspace of the UAM as destination objectives. These points act as guiding references for the sampling-based algorithms, simplifying the creation of connectivity graphs between the starting position and the intended destinations for the aerial manipulator. The effectiveness of this strategy is demonstrated across various scenarios, highlighting its superior performance in terms of efficiency, computation time, and path length when compared to existing path planning techniques like RRT^* and Informed RRT^*.