The heavy wiring on the 27 MHz Train Engineer is the INPUT wiring and was designed to power an entire garden railway. If you have a battery pack with the same connector, you could leave it in place although it takes up a lot of room even coiled and wrapped.
If you are using a switch to toggle the battery pack between its charger and the receiver, the heavy wires could be cut and soldered to the center terminals of a switch. Or if a larger switch with screw terminals is used, number 6 loop connectors could be crimped on the shortened wires.
The output wires from the screw terminals of the receiver do not have to be that heavy a gauge to run an Annie. The rear light plug wiring is heavy enough. Most of the other wiring in this locomotive is the same gauge.
In my conversion the rear light plug wiring was used to power the locomotive. As I had used the smaller 75 MHz receiver, the Bachmann sound board, speaker and plug were left in place.
The other two shorter plugs are for charging the battery packs.