Exposed wire on outdoor Christmas lights
You do not want to tape this. If that plug is going into a 120V outlet, cut it off and replace the plug with one similar to the one below.

If that plug is going into the low side of the power supply, you can get some insulated splices at your home store and repair the wires.
UPDATED
Based on the new photos, the damaged wires are on the secondary, low voltage, side. So the insulated splices would be the way to go.