Many rigs like ours have solid walls/roof/floor - nothing is run through the inside of them.
Rather, the idea of dropping a line through the floor from the breaker box, running conduit on the underbelly, then back up through the floor to the desired inside cabinet is a good one. I've used that method in our house as well, though I didn't need the conduit in that case.
If you run conduit from breaker box to the new outlet, you can use individual wires. I'd run three 12 gauge THHN wires (black for hot, white for neutral, green for ground) commonly available at your local hardware store.