I don't know the exact colour of the wire in question. You will have to get out a circiut tester and do some probing.
Your looking for one wire. Set up the tester and touch each contact on the back of the barrel one at a time.
Turn the ignition on and test some of the contacts. You should get 1 or 2 lives showing. Then slowly turn the key to start the engine, probe about and you should find 1 wire that goes live, that's the one that feeds the starter solanoid.
Cut that wire and join the 2 ends to the starter button, making sure that it's properly insulated.
Then test it again and see if the button works.
When you buy the button, make sure that it's strong enough to do the job, as there is a fair bit of current running through the switch.
Also make sure that the switch is an insulated item, as you don't want to become live yourself when you press it.
Good luck!! (but don't hold me responsible if your hair stands on end)