Purchase a MagSafe 2 Cord Only? My dog decided it wanted to make my MacBook Air Charger (MagSafe 2) his new chew toy. Is it possible to buy just the cord that connects to the charger and the MacBook Air?

I can only find the charger box (for lack of a better term) and not just the cord which is what I need.
I'm assuming you're talking about the detachable AC Cord (http://support.apple.com/en-us/ht2346) 

Amazon has one for US outlets:  http://www.amazon.com/Power-Adapter-Extension-Apple-Macbook/dp/B009OA61UK
But, it is not an official Apple part, and (especially when it comes to power supplies) you might feel safer to stay with the sanctioned parts.

Your best bet for a real cord is to find a friend with a MacBook who plugs their charger directly into the wall, and ask them for their spare cord.