Would it be bad to use a sword to kill zombies because the blood might spread the disease?
In such a hypothetical situation, there would be no blood. Without a working heart all the blood in any zombie would drain into the legs and congeal there. The edema that this would cause would eventually create fissures in the skin of the legs and feet, which would split open and expose the musculature and bones of the foot. A sword (a good one, preferably a katana or broadsword) swung against the neck in a decapitating strike would in all likelihood NOT get stuck in the neck, as the only bony structure there is the spinal column. Even if it takes more than one strike to decapitate, the odds are that the zombie will be unable to hold its head up or bite at all because of the tendons and muscles of the neck that would doubtless be severed on the initial strike.