Variation on Beka’s suggestion: Keep the currently working charger completely wrapped for use in the room, storing it up high or in a drawer until you take it out. Bring the damaged ones to a Mac store and tell them (bring as many as you’ve bought) what’s happened and how many you now own. Ask if they can repair one of the cords, then keep it in your bag only as a backup. A broken wire is a simple repair with a sauter or splice if someone knows how. It may be covered by your warranty if it’s within a year. Check it out. Otherwise, check out Ebay to get a much cheaper cord to keep stored in the bag.
If you have bunnies, you may as well get used to living a bunny-proofed lifestyle now. It will last for years with very expensive equipment. Walmart sells the wrap around plastic that is spiral, so you don’t need to cut it apart, just wind it around. An annoying half hour to do it is worth a lot of money.