Hey Anton, welcome.
I used to have a Lancia with a three-spoke wood-rimmed steering wheel, could never figure out how they made it - it did not look as if made up out of segments, but also did not look like cut from one solid piece - the grain seemed to follow the curvature. I wonder whether it was steam-bent?
I guess you would need to make two half-rims, with a routed groove in each half for the steel, then glue them together encasing the steel?
If so, it might be easier to rout the groove before cutting the inside diameter of each half-rim.
Chuck raised an interesting point about differential expansion of the wood rim and the steel core. What I remember of mine, is that it was completely solid - no expansion space noted.
As Dan says, nothing like a double somersault off the high board in order to get your toe wet.