Something you want to consider is if you parallel a remote switch with the internal switch both switches need to be off for the unit to be off. If either switch is On the unit will be on. But you can't for example, remotely turn the inverter On and use the switch on the inverter to turn it off as whichever switch you turn it on with needs to be the switch to turn it off.
Your picture shows a 500 watt inverter so if delivering full power of 500 watts discounting inefficiency of the inverter tells me under full 500 watt load the inverter will draw 500 Watts / 12 Volts = close to 42 Amps or a 500 watt surge 300 watt standard out will be 300 watts / 12 volts = 25 Amps so the wire gauge needs to be planned accordingly. My guess is the small switch pictured will not come close to those DC current ratings. The switch on the inverter is not handling the inverter load but merely turning electronics in the inverter. Purely a guess on my part.
As to the switch and mentioned earlier, a switch is merely a switch. The contacts may be rated in AC or DC but your concern is how much current are you switching. The rated contact voltage and current, beyond that it's just a switch.
Ron
Your picture shows a 500 watt inverter so if delivering full power of 500 watts discounting inefficiency of the inverter tells me under full 500 watt load the inverter will draw 500 Watts / 12 Volts = close to 42 Amps or a 500 watt surge 300 watt standard out will be 300 watts / 12 volts = 25 Amps so the wire gauge needs to be planned accordingly. My guess is the small switch pictured will not come close to those DC current ratings. The switch on the inverter is not handling the inverter load but merely turning electronics in the inverter. Purely a guess on my part.
As to the switch and mentioned earlier, a switch is merely a switch. The contacts may be rated in AC or DC but your concern is how much current are you switching. The rated contact voltage and current, beyond that it's just a switch.
Ron