You might think again about changing the circuit.
As I understand the operation once the ignition is turned on a magnet is brought up to the reed switch causing the relay to latch and power the shutdown relay.
I think the purpose for the second contacts on the output is to protect the reed switch from the inrush current of the shutdown relay. Reed switches are typically only rated for 10 to 50 milli-amps. With the current circuit the reed only has to momentarily handle the current for the latching relay, but never will see the heavier current from the shutdown relay.
Good luck
If you do want to try it and make the change just connect the wire on terminal #4 to #5 instead. But as noted above I would expect the reed switch to soon fail.
Dave