If you can find a car that already has a remote control, then you could remove the foot pedal and replace it with a button for the kid’s head and that would be the simplest electrical work.
@mikey has designed circuit boards to adapt from the plugs on many foot pedals to the audio jack on adaptive switches and this would let you avoid soldering, but you could also just connect the button wires to the pedal wires with a solderless method of connecting wires (maybe screw terminals or crimp connectors).
The car Matthew posted says on the website that it has a remote control. I don’t know if that includes steering, and I don’t see it on Amazon.