You can mostly figure it out using the illustration on page 5 of the Order Guide
The Cayman Club - Downloads - 2008 order guide
The base vehicle interior description on pages 2 and 4 says "Steering wheel rim, gear selector, hand brake grip, armrests in the door panels trimmed in leather." Then look further in the order guide to find the descriptions of each part to see if you ordered an option that says it is leather. Otherwise it is probably plastic.
I worked in the plastics industry many years ago. Only a small amount of the plastic in the Cayman is vinyl. The door panels and sides of the seat covers in the non-full leather cars is vinyl. The non-leather dash cover is more like a rubber product. Virtually none of the hard plastics inside the car are vinyl. They are usually polycarbonate, ABS or polypropylene. I am pretty sure that none of the exterior plastics are vinyl.
I use Lexol Vinylex in the interior on all plastics (hard and soft) for a non-gloss sheen and One Grand ERV or 303 Aerospace Protectant on all the black exterior plastics. I prefer the high-sheen (non glossy) finish that One Grand ERV leaves, but I think the 303 may provide better UV protection. (I am not a chemist, so this is just a guess.)