I don't know if we'll have the funds of material for a good sword, but it doesn't hurt to look. A dagger, at the very least, would be helpful. you're not exactly a ranged fighter.

[And while building skills is always good, you should build on what you know first. The fan is a close-range weapon.]

As long as you're fast and you know where to aim, you should be alright even with a shorter blade. Just remember Lee Chang's words. If confronted with the undead, aim for the head.