Specifically, the pressure is around 200 PSI. I get the impression from what I have Googled that .006 and below may only work for high-pressure systems.
To answer your original question, I would guess that a .006 would not work with a mid-level pressure system. It appears that the smallest size would be .012" for the mid-level pressure system.
This write-up for a .008 orifice (which is larger) states that it should not be used with pressure below 250 psi. So the .006 would definitely need a high-pressure misting system, i.e.,1000 psi.
Also most of the specifications for .006-008" orifice by the major misting vendors are associated with high pressure system usage.
The .006" is the smallest size listed for high-level systems (750-1000 psi) so it is highly unlikely that it would work for a mid-level system at 200 psi.