Brilliance version 2 (I believe) dropped the dongle. Really, there is no good reason to be using version 1 anymore.
So, what exactly is the danger of hot-plugging the joystick port? It's not the switching of the devices itself (although that can cause physical fatigue on the port), but rather the risk of static discharge when doing it, and also the risk of inserting something sloppily and shorting the wrong pins, right?
So using a joystick/mouse switch-box shouldn't cause any problem, because switching of all pins on the port is instantaneous and there is no human contact with the pins/grounding plate of the joystick port.