Not sure of the exact wiring but one will be a perm live,one switched,one to starter and a negative cable.best to identify them using a multimeter plus you'll need a hefty switch or a wire in a relay as the starter does draw a lot of current although your starter button kit should provide this.
Beware you will still need the key in or around the area of the black ring with the thin low tension wires as this is your PATS immobiliser system and it will NOT start if it doesn't sense the passive transmitter in your key (the little red tab on your key houses this).
I've seen people tape up the key near the pats ring so the car still starts but you do lose your immobilser then as effectively anyone who finds your ignition system could just start the car.
I've never actually done it,but I've toyed with the idea of soldering wires to extend the switch to a hidden location and just use the key to unlock the steering and then the push start to fire the car up.