I used corrugated plastic sheets doing something similar to what you're aiming to.

First I built-up the frame screwing 10mm (3/8") ply strips to the edges and then i screwed the coraplast to the ply.

For the doors, same thing, ply frame with diagonal strips to add rigidity and keep everything square, coraplast on top, plastic handles and thin folding hinges or a strip of piano hinge.

You can then use thin plastic angle profiles to make the corners prettier or simply use silicon sealant.

I couldn't be happier about the the way they turned out. Reversible, extremely lightweight, durable and super easy to clean.