The airbag cover is different for both models, so you need the one for the one without the, that is if the airbag module isn't permanently attached to the cover. The airbag cover extends over the audio controls and plastic trim piece on the opposite side, so there isn't a plastic piece where the audio controls or the corresponding piece on the right side. You will most likely need to replace the airbag module. From the looks of it, you could keep the leather wrapping, but need the airbag module.
I looked into replacing my wheel with the leather and audio controls, but decided it wasn't worth the cost.
Here's a picture of the wheel without the controls to give you an idea of where the controls are supposed to be.