I don't have the answer to square footage, but I'm wondering a couple of things. First, how will you fit vinyl into the corners without lots of unsightly seams? Second, without any insulating material, how are you going to control condensation on a cool night?
Glenn's point is that the shell requires support from the interior cabinetry to maintain its shape. Without it the shell will sag and bulge out in the middle, resulting in poor door fit and other issues.
You can support it during your reno with a 2x4 between squares of plywood on the floor and ceiling. In your finished layout, make sure to include floor to ceiling support, especially near the door. Cabinets can serve that function, or for a more open layout, you can
fiberglass ribs to the shell to provide support.
But do think about some kind of insulation. You don't want condensation dripping from the ceiling while you sleep.