I called Bali, the manufacturer. They were able to look up my order based on the number on a sticker on the blinds. They said the entire headrail needs to be disassembled to replace the cord. They cannot send me a cord and instructions. There is a lifetime warranty, but since the previous owner purchased it and my name was not on the warranty, the warranty is invalid. It looks like I am purchasing a new blind. They said you could buy just the headrail, but my wife would like a different color if we are going to have to take it down anyway.
If anyone has one of these blinds and you know who purchased it. Make sure you use their name when you call or email them.
Best Answer
Looks like a "wand tilt control".
http://www.fixmyblinds.com/vertical-blind-tilt-controls-s/91.htm