If the laptop has a battery installed, cranking should not be an issue (it would be like pulling the plug for a second then plugging it back in).
As for wiring, it's pretty simple. Here's what you'll have to hook up for MOST shutdown controllers (read the instructions for your SDC carefully first!):
-constant power IN, should be directly from the battery
-switched power IN, eg. the ACC line, this tells the controller when to send the on/off pulses to the power button
-power OUT, this will be going to your inverter so that your laptop can be charged by the inverter
-(may or may not be) ground "OUT" for the inverter, you may also just ground the inverter to the chassis (remember to use a single ground point for everything)
-2 pins for your ATX switch, these go to the power button that you've soldered on to, polarity should not matter so either pin goes to either pad on the button
Hope that makes sense and helps you a bit.