Yes, that would be acceptable! You can assume his arm can no longer be used for any powerful attacks and give him the sword. Your other option is to keep the overdrive attack on his arm with no sword to start with, then work toward having him earn a custom crafted sword in-game as a plot if you want, meaning he could eventually "level up." It would just need a little plotting to obtain since its purpose is to unlock some additional powers for him.

Either would be fine depending on how involved you want to get!