During the COVID-19 pandemic, the spread of infection through shared pens and touch panels during signing became a societal issue. To address this, we developed a contactless signature system. With touch panel signatures using fingertips, signers can directly see their fingertip position. Aiming for equivalent intuitive operability, this research developed a system enabling direct signing onto an aerial display. Two web cameras detect the 3D position of the signer's fingertip during signing on the air display and project its trajectory onto the display. First, to build a prototype system, we evaluated the optimal placement angle of the front camera. Through subject testing, we determined that an angle of 15° from the horizontal plane, where the legibility rate of the three-letter alphabet “TCU” reached 100%, was the optimal position for the front camera. Subsequently, the system's accuracy was evaluated through two participant tests: tracing accuracy and recognition accuracy of the position of the aerial display. The tracing test revealed discrepancies between the participant's intended starting and ending points and the system's detected points, leading to overdrawing or missing strokes. The recognition accuracy test highlighted the difficulty humans face in accurately perceiving the position of an aerial display.