Original Deluxe Steering Wheels were never real wood ; always simulated wood, plastic. Some years ago, a company (I can't remember who it was), made a nice imitation out of real wood. This is what I believe you have. The good thing, you'll not have to worry about the plastic cracks opening up as happens many times on originals.
And yes, the Deluxe Steering Wheel was a Factory Option in 1965, but in 1966, it also was available as an Accessory (attached from the 1966 Accessory Catalog).
Bob