solder two more wires on to the little switch, and run one wire to the TX wire inside the mic, and the other to the shield wire inside the mic.
then the switch will be "closed" whenever you key the mic, or when you push the button.
the mic will be useless for anything other than tweety birding though, as it will make noise the whole time the mic is keyed.
if you want it to just tweet for a second, thats a new circuit you'll need to add.
LC