Fist question, do you KNOW he gave you the wrong cape, or do you just THINK he gave you the wrong cape?
Second question. What purpose would there be to removing the cape and mounting with a new one? It still wouldn't be the original. Maybe I'm missing something.
The answer is maybe. More often than not, the best way to go about it is to just remount the whole thing. It seldom makes any sense to try to remove a cape apply a new one. It's much faster to just start from scratch.