However, I found a nice little free utility that can do it, and I thought I would mention it here.
AutoHotkey
You'll also need the script that reports which joystick button is being pressed:
Joystick Test Script (Save As)
Here's the script I'm using at the moment. It binds joystick button number 12 (one of the buttons on the base) to left-mouse-button.
Joy12::
Send {LButton down}
KeyWait Joy12
Send {LButton up}
return
Easy way to make a floor-clicker out of an old joystick.
