Wont be able to stick weld something that thin, you will just blow a hole in it. MIG welder will probably also have a bit too much heat to weld that material, might be able to get away with tacking though. TIG (Same as GTAW above) would be the way to go but it requires more hand skills than MIG.
But as listed above, galvanized is nasty nasty #### to weld. You could try buffing the back of the plates and then tacking the corners but it would still be good to get some sort of respirator.
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