The point can be moved by changing the weight distribution.

It is conceivable you can put the center of percussion at the tip of the sword - this happens when you swing the sword (assuming it is a uniform rod) about a point that is $rac13$rd of the way along the length. Many medieval swords had a heavy pommel - not only to make it harder for the sword to slip from your hand, but also to increase the moment of inertia and thus move the center of percussion (the center of rotation of a sword is typically not the end - if you 'flick the wrist' it will be inside the sword, while a broad swing from the shoulders with straight arms might move it further back). The exact location of the center of percussion depends on the geometry of the sword. This is achieved when you hit at the center of percussion: the point along the sword where you would feel no 'twang' when you hit (on sports equipment like bats and rackets they call it the 'sweet spot').

If cutting off the zombie's head is an inelastic collision that requires the greatest transfer of momentum/energy, then clearly this will be achieved if the sword stops moving completely at the end of the stroke - if the sword keeps moving it still has energy / momentum that wasn't used to chop off the head. UPDATED now I am near a computer and can draw diagrams etc. But there's a point in between these two that works even better exactly where that point is depends on how you swing the sword, and how its weight is distributed. If you have to choose either 'near the handle' or 'near the tip', the tip will work better.

How to swing a katana