So for Christmas I got my wife a king size heated blanket. She absolutely loved it. Unfortunately a two weeks ago we also got a new dog and it started using the cord as a chew toy. What would be the best way to repair this connection? Ideally I would like to cut all four wires and reconnect them but I am not sure what voltage they are carrying. The wires appear to be 16-18 awg if that helps
I'd inline splice & solder it, then heatshrink.
Use some heat shrink tubing, spread the wire enough to hold the heat shrink. inline wrap the wire to its mating side so that it stays flush in the lengthwise of the wire, then solder it. Then heat shrink each over the repair.
This will reudce the likelyhood it pulls apart, keeps out moisture, and is electrically safe.
This is not 100% how I explained it, but google inline splice wire, and you will see numerous pictures to get the idea: https://www.instructables.com/id/Soldering-Tutorial-Inline-Splicing/