That seems... counterproductive? But I won't knock your methods if they've gotten you this far. So the swords are swords and you can use them no matter what, it's just whether they're currently worth bleeding for that's up for interpretation.
Even if they do work, I think you'll have to figure out whether bleeding with zombies prowling around is worth it. For you and everyone else. I don't even know if they're drawn by blood, but it seems like something they'd like.