You can first measure the current when switch is closed by powering with a multimeter set on current range (if you have a multimeter).
But since you disabled the voltmeters the current through the switch when ON should be very small not a problem for EXT IO3
Both the switch on the unit and the one on the remote are one and the same thing they are just in parallel so you can connect the EXT IO3 to either one depending which one is more convenient for you
If you need the ability to turn OFF the inverter add the EXT IO3 in series with the switch.