Yes, it's better to migrate over to 12V LED's than try to puzzle out or change fixtures. There are LED panels that have a self stick tape on the back. You can use the same wire, once disconnected from the 120V source.
FWIW, I made new LED fixtures using a card display holder, purchased at the Dollar store. I cut a piece of light aluminum sheet to replace the cardboard easel they came with. For bulbs, I used LED panels in varieties of illumination for the spaces they light. For <$4, I'm real happy with my lights.
