So long as your inverter isn't grounded then the outputs are floating and not referenced to ground, making them inherently safe like small generators.
The only way of getting current to flow would be for you to touch both Line and Neutral.
Choose an inverter with clear documentation so you can be sure that it is not grounded through the 12v ground.
You shouldn't need any external wiring, inverters are really designed to be used with devices plugged directly into them.
If the inverter you are considering doesn't have overload protection built in, choose another inverter.