Modeling the wheels is necessary for a reasonable simulation, even if the user doesn’t see them.
(You just don’t need to make them pretty if that’s the case! Unless there are reflective surfaces.)
Interacting using buttons, could be as easy as using the Widget Component to put a 2D UI panel in the 3D world that the user can click.
You will need to read up on some of these things (use the google for the appropriate keywords) to get there, but unfortunately I don’t know of any shortcut around that. It’s totally possible, though!