[Al Skierkiewicz]

Joysticks use the interface to provide a calibrated PWM signal to control the speed controller per the hobby PWM spec for radio control. Some teams have managed to make a simulator using a 555 timer as a PWM generator. If you are going to control more than one motor, it becomes a little complex to use the 555 solution.
As to the solenoids, the switches in a joystick cannot sustain the current needed to drive a solenoid directly nor are they locking style switches. They are momentary only. You can use off the shelf switches from almost anywhere if you just want to turn something on and off. Even Radio Shack has some automotive switches that are suitable for this purpose. Please be careful in your cart design to be sure that no one will be injured by the cart movement in a tight pit area. More than one team has been asked to remove all power (electrical and pneumatic) from a cart due to it's potential to injure participants.

Thank you Underwriter Lab volunteers for keeping a look out for this issues.