Mart, I think that those nebullizers are also using an ultra sonic fogger in them. But you can buy the fogger alone cheaper. It costs about 30$ on ebay.
Anyway, I put this circuit together. Instead of inverter I am using a variac. The capacitor is 150uF 400V and all the diodes are IN4007. There is no sparkplug, just two bolts with the flat sides facing each other. The air gap is about 0.5mm. The capacitor is very leaky so I need to fire it just as I turn off my variac. Got some nice bangs. Then I sprayed a little water over the electrodes. They got wet, but there were no water drops formed between the electrodes so that they are touching through water. The wet electrodes gave a bit bigger bang than when they were dry, but I could hardly see any difference in spark appearance, maybe it was a little more red or yellow, but it is gard to tell. I am thinking that maybe we could put the spark gap above a can of boiling water, so that when the steam comes up and through the spark gap, we could fire it.
Here is my setup:



Those are two neo magnets attached to the + terminal of the cap.