You might have to work in an informal expression in some other way besides direct substitution.

There is an expression "behind the wheel" but without knowing the sentence I don't know if that works.

There is the word "trucker" but it doesn't apply for passenger autos.

Can you give us the full sentence and I can try to recast it?

Probably, you can't find one word that will be an exact fit for the Russian equivalent on all occasions and in all situations. Sometimes, "cabbie" (hack(ie), etc.) is the word but only for taxi drivers. "The trucker dude" may loosely fit but only if you drive a truck. Sometimes, "the guy (dude, etc.) behind the wheel" could work. Sometimes, none of them will work and you have to do as Deborah Hoffman suggests, etc.

Driver is the general term for anyone who is driving, no matter the vehicle. I would use "trucker" when referring to commercial trucking, but you could also use "driver" there, unless you want to be specific. "Cabbie" or "cab driver" for taxis.

"A fourwheeler" is a vehicle ( like a hackney coach) with large tires.