You really can't do this without opening the case. The case can be opened. I've done it several times to replace the magsafe cord off the end of them. To do that, the best way I've ever seen and the way I do it is stick pliers into the void where that wing goes and spread them and force it apart. Be careful, you DO break that plastic apart and you'll have to superglue the whole mess back up when you finish.
Seeing as you've got to further break it to fix it, I might just fly with one wing or go into the apple store and ask nicely if they will swap it out. I've heard they're kinda lenient on those.