How can I wirelessly duplicate a lighting switch
Why make it more complicated than it needs to be?

What you really want is a switched-hot and matching neutral to power the undercabinet lighting from.  Well, they're right there at the switch box, since that's where power comes in at.  Using a pigtail and wire nut to tap the switched-hot, and tapping the neutral at the existing junction, going off into a /2 cable to the LED undercabinet lights, and that's all that's needed.  No need to fuss with wireless switches or any of that, just a cable (or surface raceway/trunking with wires in it if running a cable through the wall isn't an option) from point A to point B.