As I understand it, WS has (at least) two types of pre-lit buildings. One accepts track/accessory voltage AC or DC and had internal brightness adjustment controls for each LED. Here's a photo swiped from this OGR thread
Another type uses a Just Plug Light Hub which is external to the building box for brightness adjustment. The Light Hub also accepts track/accessory level voltage.
LEDs operate at around 3V DC. So if you are starting from "only" 4.5V DC from a Menards adapter, you don't need the relatively large voltage reduction function of the above two methods. I'm not aware of any plug-and-play boards/modules that have the correct connectors and voltage reduction function. But the electronics of such a reduction could be as simple as a 5 cent resistor...or a 25 cent variable resistor if you want brightness adjustment. This involves working with small components and in all likelihood soldering which is not in everyone's comfort zone. But this DIY approach can be discussed further if there's interest.
When rolling your own, having the right connector is always handy. On the Menards side, you can get screw-terminal adapters so you don't have to splice into the plug wiring.
On the WS side, there are wiring accessories that have the LED / Light Hub connectors.