We tried something remarkably similar, actually.
Zombies don't get guns and get 'kills' by tagging humans. Humans 'killed' go down on one knee and count to thirty, after which they respawn on the spot as zombies.
Humans are armed with sidearms (or cqb weapons on semi) and with close combat weapons (foam swords, fencing weapons, etc) and must shoot or tap the zombie's head to score a kill. The melee weapon is to prevent point blank face shots, but zombies are nevertheless encouraged to wear face protection and/or helmets.
The game starts with one 'alpha' zombie per five humans. Zombies have their own spawn point which the humans aren't allowed to approach. Alpha zombies spawn here, and newly infected zombies start spawning here after the first time they are killed (when converted, of course, they spawn where they were tagged)
The game goes on until the humans achieve their objective, or until the zombies kill them all.
Game types:
Death match: zombies get 3 lives, alpha zombies get 4, humans get 1. Fight to the death.
Evac: The alpha zombie hides a timer set for five minutes. The humans must find it, activate it and defend it until the five minutes expire (the zombies can't stop it, but they can kill all the human defenders).
Notes: the game only works in periods of poor visibilty, like fog or at night. In such circumstances, humans wear glowsticks and zombies don't. It also works better if the humans are forced to split up for whatever reason.
And zombies are encouraged to yell 'brains' whenever they feel like it.