I have not used that type of paint. In general you want to avoid paints rated for exterior use simply because they have to be more flexible to deal with expansion and contraction. For vapor and moisture resistance you always want to use the hardest finish that can withstand the natural flexibility of the surface it is being applied to. In your case an interior bathroom paint will be more durable, although that does seem counter-intuitive. But if you already have the paint, I guess go ahead and use it.
I would not use 1/4" plywood for this project. You might be able to get away with 1/2" for the sides and 1/8" for the back (which is the equivalent of use 1/4" for the whole thing), but definately use 3/4" for the horizontal members. And build some sort of face frame to support the front.
I would like to get Bighurt's opinion on this, however.
If weight savings is your goal, try building it from hollow core doors. You can often get tear outs from remodels or scratch and dent doors from home centers for very cheap. They make for a very flat, strong and light building material. Sealing up the cut ends is the only part that requires some patience.
Even at prices for brand new HC doors you really can't find a lighter and cheaper building material.
I recommend HC doors with interior frames made from finger-jointed pine. This is easy to see on the outside edges. The particle-board framed doors are not as nice to work with.
But really, look around for old or damaged HC doors. I could have probably purchased a hundred of them in the past year for about a $7 each average. No kidding.
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Current snakes:
0.0.1 Gonyosoma oxycephala - Java locale (green)
1.2 Gonyosoma oxycephala - Jave local (green)
2.2 Gonyosoma janseni - Seleyar locale (all black)
1.2 Gonyosoma janseni - Celebes locale (Black & Tan)