I think the plywood would be okay, you would have to season it with a few hours of smoke., You could always also, line the inside of the box with aluminum flashing and some good silicone in the corners. If I were to build one I would find reasonably priced racks and build it to for them into. also have some supports for some 3/4 wooden dowels to hang things from. And adjustable damper, and if your are really ino it maybe a small computer type fan with a dimmer switch so you could control air flow.
If you have access to good pallets, you could use them and fill in the open spots, and build your box.
For smoke, 3 ways that come to mind, would be an one of the cold smoke tubes or trays. I use my tray more than my tubes. I use from this company (
https://amazenproducts.com/ ) He also has bulk Qmatz material, if you sign up for emails he does discounts most of the time.
Google Mailbox mod smoker, still uses a tube but is outside the chamber.
You could also find a low wattage hot plate and old cast or steel skillet to use with dust.
For things to cold smoke other than cheese. Butter, bacon, sausage, hams, peeled hard boiled eggs, just about anything you want to toss on the grill to cook, steaks, chops, burgers (an hour or two in the smoke then cook them) salmon and fish.
Hope to see it when you are done building and what you smoke in it.