The LED-Wiz would work fine, but may need a small relay in-between, depending on the way the fog machine works.
Just a note about the fog liquid (couldn't resist). The PG used in fog machines is pretty much the same component used by "E-cig" smokers in their flavored liquids. A few have complained about allergic reactions, but these are more often than not the result of directly inhaling the vapor, over very long periods of time. Still, there may be safer alternatives, such as vegetable glycerin, or a mix of the two. VG creates a heavier vapor, which tends to hang longer in the air, but may be of less concern health wise. It's also good to use USP grade liquids if the fog is somewhere where it is likely to be at face level.
RandyT