To me it depends on what kind of zombie is in your game...
1) romero style zombie be it fast(first 24 hours after death) or slow(after rigor sets in) needs only teeth because it's only function is to make more zombies by infectious bite.
2)cursed zombies protecting an area may use weapons if their only purpose to kill trespassers not add more to the group.
3) cursed(movie voodoo) zombies have insane back breaking strength to kill the target of their makers wrath and are immune to weapons without a specific component needed to end them(such as salt in mouth covered with holy wax etc...) with no need to bite or use a weapon to kill.
4) raised zombies to be used as troops use what weapons they had in life and are used to attack other armed and armored living troops usually without the need to make more of themselves by such mundane means as biting to infect.
that's how i see it anyways.