You can add a little 5V relay and wire in a 5v power brick to the mains power. Wire the 5v out to the coil on the relay. Wire the switch pins in the relay to each side of your switched circuit.
Then, once power is applied, the power brick usually has a short delay (0.5 to 2seconds) between the time the brick is energized until it delivers 5v power. That delay should be enough for your humidifier to start up and be ready for the switch to apply.
One condition, you'll have to make sure it works with the switch applied the full time or if you need to pulse the switch. If pulsing is the answer, then we need more circuitry.
Note, get relay that needs very few mA to stay in the "on" state so it doesn't overheat at the coil.