Omnidirectional aerial robots offer full 6-DoF independent control over position and orientation, making them popular for aerial manipulation. Although advancements in robotic autonomy, human operation remains essential in complex aerial environments. Existing teleoperation approaches for multirotors fail to fully leverage the additional DoFs provided by omnidirectional rotation. Additionally, the dexterity of human fingers should be exploited for more engaged interaction. In this work, we propose an aerial teleoperation system that brings the rotational flexibility of human hands into the unbounded aerial workspace. Our system includes two motion-tracking marker sets--one on the shoulder and one on the hand--along with a data glove to capture hand gestures. Using these inputs, we design four interaction modes for different tasks, including Spherical Mode and Cartesian Mode for long-range moving, Operation Mode for precise manipulation, as well as Locking Mode for temporary pauses, where the hand gestures are utilized for seamless mode switching. We evaluate our system on a vertically mounted valve-turning task in the real world, demonstrating how each mode contributes to effective aerial manipulation. This interaction framework bridges human dexterity with aerial robotics, paving the way for enhanced aerial teleoperation in unstructured environments.