I have the same problem. My cats have an appetite for apple wires, in particular the soft thin wires used for the Iphone and Macbook chargers.
SOLUTION:
There is no solution for your iphone charger wire. The contents of a USB type wire are a set of very small thin wires that are (near) impossible to strip. Even if you succeed, chances are that connecting them will not result in a fixed wire, probably due to the sensitive nature of the USB connection. However, for your Macbook charger the prospects are less grim and these wires can be readily fixed in 15 minutes. The wire consists of 2 coaxial wires, which on their turn consist of a bundle of very thin wires. One is wrapped around the other with an insulator in between.
1. Cut out the damaged part of your wire. Try to save as much good wire as possible to preserve cable length.
2. Strip about 2cm from the ends of the now 2 separate cables.
3. Bundle the outer thin wires with your fingers by simply wrapping them with a rotating movement. Be careful not to pierce your skin.
4. Strip 1 cm of the inner insulator wire.
5. Weakly bundle these wires as you did with the outer wires.
6. Now you can opt for either soldering the wires or using a screw terminal to connect the wires. The soldering usually gives the best result. When you choose soldering, you can shove the bundled small wires together for a better connection. Either way, make sure that the inner and outer bundles do not touch eachother.
7. Test the connection. If it doesnt work, it is probably caused by the bundles touching eachother and shortcutting or the wire being broken elsewhere additionally.
8. Use electrical insulator tape to insulate both the soldered bundles from eachother and to cover the rest of the exposed part of conducting wire.
9. Cover the connection with an extra layer of duct tape or other tape for some extra protection.
Done.
PREVENTION:
I have found out that all this misery can be prevented by covering the wire with duct tape. Simply roll off the duct tape for about half the length of the cable you want cat-protected, then cut/rip the tape in half over its length and wrap it around the cable. Your cats will probably loose interest, are unable to chew through the cable and/or it will buy you more time to intervene.
Good luck.