If you mess with the pinion gear and such, you will have to reset the clearances or it will not run right. But you can just take all the internals out and use them in your 8.8 providing the splines are the same as was mentioned.
BUT, the easiest thing to do, especially if you have never installed gears or do not have someone experienced to do it for you cheap.....is to remove your rear end from the car, remove the axles, brake lines and brakes from your 8.8 and the Cobra 8.8. Install your Fox axles and brakes on the Cobra rear end and install it back in the car. The rear end housings are the exact same size for all 8.8 Mustang housings from 86-98 and are interchangeable. All the brake and axle parts will interchange with ease. You will keep the same width and get the good diff parts without messing with the gear install. It might take a bit longer than swapping the gears, but IMO it is a better deal than spending several hundred dollars on having a shop swap the gears and diff over. Then you still have a good Mustang rear end with intact and setup gears you can sell to someone else. Of course this all depends on the splines being the same.
Good luck!