Wireless Unmanned Aerial Vehicles (UAVs) were introduced in the world of 4th generation networks (4G) as cellular users, and have attracted the interest of the wireless community ever since. In~5G, UAVs operate also as flying Base Stations providing service to ground users. They can also implement independent off-the-grid UAV networks. In~6G networks, wireless UAVs will connect ground users to in-orbit wireless infrastructure. As the design and prototyping of wireless UAVs are on the rise, the time is ripe for introducing a more precise definition of what is a wireless UAV. In doing so, we revise the major design challenges in the prototyping of wireless UAVs for future 6G spectrum research. We then introduce a new wireless UAV prototype that addresses these challenges. The design of our wireless UAV prototype will be made public and freely available to other researchers.