My beef with an axe would be if there are a couple zombies and you got it stuck in the head of the first one, the other one would be all over you. If the blade has some stick preventing contour to it, it might be ok though.
Wait, you were afraid of not being able to use a sword because you wouldn't have the strength/stamina to deal a killing blow. Now you are getting axes stuck in zombie's skulls. If you are this strong now maybe you should fight with two axes.
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