I don't think you need the chair. Plywood is really easy to shape, just soak the wood in water for a couple of days until it is soft enough to bend it to the shape you want. Bend it over something which has the form you want the plate to be and fixate it with a clamp or whatever suits. Than leave it to dry completely, you can put it close to the radiator or something but do not try to dry the wood to quickly, e.g. by using a heat gun.
You don't need really thick wood, 4mm should be ok. It you want to laminate it with glassfibre 1.5 - 2 mm should do.