When I worked leather, I soaked it and stretched it into shape, and let it dry in that shape.
I've never had anything to do with swords, but I imagined that the scabbard did not slide entirely into the frog, so that the weight of the hilt would tend to counterbalance the angle at which the sword hung. Interesting problem. You could try the soak-and-dry technique over a frame or dummy with the sword in place. Let us know how you get on.