If you want to melee a zombie, you better know a few things.
They will try to bite you. To use a sword you will need to be close to them, so you will give them a chance to bite. Ofc if you don't have any way to escape, having a sword still better than nothing.
They are more powerful than a human. Read this:
http://entertainment.howstuffworks.c...e-strength.htm
It explains how can humans lift a car in extreme situations. We've never seen a real zombie, but they're probably capable of using their muscles at maximum, becasue they don't feel pain, their brains no longer limites them in any ways. However I don't know if zombies have adrenaline. If they don't, you might be saved from 10x muscle power, but still they will be able to use their body more, becasue they don't feel themself tired.
You will be the one who feels fear and not them. You can arm yourself as much as you want. They will keep coming.
I only see one way to be safe between them. You need no weapon, but armor that protects you from their bites. Suits made to use on a motorbike are great. You can take much harder hits with that. A full suit can protect most of your body. Add neck protector plates and some kind of gloves that cannot be bitten through. Dog training gloves maybe. And make sure your helmets cannot be removed easily. If you have enough money you may buy kevlar bulletproof armor too.
I'm also thinking about buying a sword becasue I like them. Fantasy and anime did this to me
But I never though about using them in a zombie attack XD