Probably the simplest, cheapest solution would be to purchase a sound effects keychain fob from a place like a dollar store or K-Mart. these usually have several sounds like machine gun, rocket, bomb, explosion, etc. You could dismantle it and wire the switch to one of your spare stick buttons.
Beyond that, it is now possible to get small recording/playback chips (like from greeting cards) and record sound files to them from the Internet. Best place to find info on this is from a sci-fi props enthusiast site, like this one:
http://www.valhallaarms.com/technology/sound_fx.htm
You could also use one of those little voice recorders that are sold for recording ATC.