I've played in a game just like that. It used D20 Modern instead of CoC, but it went pretty well.
A good start off point would probably be a 'prologue'. Instead of 'you wake up, everything's gone to hell', why not give each character a brief chance to introduce themselves in a short scenario (like a 'flashback, ala Fear Itself/Esoterrorists)?
For example, the HVAC guy could have been called out to do some repairs, maybe do a bit of BS with a buddy or the client for some characterization work, and overhear, via TV or radio, some hints that not everything is going as well as it should be. A news report on a 'possible new outbreak of flu virus?' might work.
As far as systems, I think it really all depends on how you want the zombies to feel, power-wise.
If you go with D20 Modern, they'll be the traditional shambling slow zombies that are only a threat in huge numbers. The PCs will be able to tank a 'hit' (which would really be more like 'it almost bites you, but you get your plank of wood/gun in the way just in time than 'you get bit but don't give a shit 'cuz you got so many hitpoints) or two, so aside from being swarmed, the bigger danger will be from other humans. This would feel appropriate for The Walking Dead.
If you go with Call of Cthulhu, characters will be a bit less capable in combat, and more fragile. It would, however, allow their individual skills to shine a bit better, as the CoC rules are more versatile for that kind of thing.
GUMSHOE/Fear Itself/The Esoterrorists wouldn't be a bad choice either. The Esoterrorist rules would give you a kind of middle between D20 Modern and CoC. The characters are still capable, but they're not going to be cleaving through a horde of zombies with a sledgehammer, and with the 'spend a point to do something awesome with your skills' mechanic, it'd also allow the individual skills of the players to shine.