Whether you are flying Pixhawk in HIL mode or using the PX4 SITL mode on Ubuntu, you will not be able to manually fly the drone unless you have some sort of remote controller, either a real one, or a joystick that can be configured to behave like one.
There are many remote control options that you can use with quadrotors. See PX4 RC configuration for infomration on setting up remote control with PX4.
We have used FrSky Taranis X9D Plus and Futaba 14SG with AirSim.
You can also use an xbox controller, it just won't be as precise as a real RC controller. See xbox controller for details on how to set that up.
A Playstation 3 controller is confirmed to work as an AirSim controller. On Windows, an emulator to make it look like an Xbox 360 controller, is required however. Many different solutions are available online, for example x360ce Xbox 360 Controller Emulator. Note: don't use x360ce if you have a real XBox controller.
Nils Tijtgat wrote an excellent blog on how to get the DJI controller working with AirSim.