first of all, do you need time for the system to shutdown like a regular computer, or can u just switch off instantly ?
if u need a shutdown phase, you can use a flip flop gate.
a flip flop is basically an IC that u connect like this:
put key ignition"ON" on A, and it will keep supplying battery power to "1" until B is pressed.
put ignition "OFF" on B and that will give power to "2" which you can connect to the device turn off button.
basically, as long as its connected to the battery + and -, it will always provide power to either "1" or "2", depending on what you press (electronically press i mean, not physically)