In that case you need to rig your characters to the default SDK Skeleton to use the default animations and mannequin setup.
What you then need to do is to create a biting animation and if you want you can also create a hit animation. So that yor zombies can bite and hit.
Then you need to create a weapon script (xml, look into the rifle.xml for an example. Since you are going for a melee "weapon", you don't need to care about bullet classes, ammo, zoommodes, recoil, e.t.c. So a basic xml file will work fine).
Inside the xml you will need to define a "melee"
tag for the "weapon" and set the damage e.t.c. there. Also you will set tags for mannequin.
Now to the mannequin setup:
Look into the rifle setup for detailed information about weapon setup. But for your own weapon you will just need to create a melee fragment id. Inside that, you can then create fragments. If you have multiple fragments for the same thing, the engine will randomly choose one of them. This is useful to create some variation.
In our example, you would create two fragments inside the melee fragment id. The first one will be the hit animation, the second one the bite animation.
Now you can place an ai into the level, switch the model to your .cdf file (which is your custom character) and assign only your melee weapon to it.
After that, you need to look into modular behavior trees. You can assign one of them to the ai inside the ai's properties in the editor. But for this zombie, you would need a custom behavior tree.
So you search the behavior tree documents inside your project folder and create a new one (an .xml file). Just copy the default behavior tree into your custom modular behavior tree and look through it. Most of it is not needed. You can delete most parts. For example the parts where the ai is told to take cover e.t.c.
Now you just need to modify the part where the ai "approaches the player and shoots". You replace this with "run to the player and perform a melee attack".
I hope that I could be of use. Manuk also wrote a great tutorial about melee weapons, where he creates one for the player and explains the weapon xml structure e.t.c. You can find it here:
https://www.cryengine.com/community_arc ... 1&t=134962