No no no. Here is what you do. Go to a hardware store or Walmart. Buy an outlet for a wall. Right next to that they should sell a box that goes in the wall and holds an outlet or switch.
Buy one that is two wide. Put an outlet on one side and the dimmer on the other. Then cut the end that you plug something into off. Then you wire that all up so that you have a cord you can plug into the wall going to a box the extension cord goes in the back and wires up to the dimmer and outlet. Then you can plug both UTH's into the outlet. Message me if you need more info, I can post pictures.