there is a switched 120v 14 gauge wire
What does that mean exactly? There's a pigtail of Romex wire?
Unless there's complications I don't understand, I would just take the LED supply and cut off the plug. Then, use wire nuts to connect the exposed wires from the supply to the wire you have under the cabinets.
Alternatively, I suppose you could take that wire under the cabinet and wire in a socket. You'd probably want to make a cutout and put the box up inside the bottom of a cabinet in the corner. Then, you'd have a switched plug under the cabinets that you could use for anything including the LED power supply.