The best and safest solution would be to use a relay. I know you said you don't want to use one but it appears that switch is after the DC is converted to AC. At that amperage you don't want to remote that switch up to the front and risk knicking the wires. Get a DC automotive switch, an automotive relay (DC 25 AMP) and a fuse. Place the switch up front and wire it to the relay in the back. Take the fused Vcc and run it to the relay and then from the relay to the Vcc in on the inverter. Leave the switch on the inverter always on. Done.
I could give you the RadioShack part numbers if you have one in Europe.
(BTW both of the wires on the switch are black because it is AC)