Intruder, Nanoinfector, and maybe even Demolisher nanites (with a Nanoinfector vector) would be a pretty good way to wipe out a CZ unless, of course, he's got a nanite hunter system onboard keeping him clean. Chemical weapons may really be your best bet here.
Going after a cyberzombie with small arms makes me laugh. The armor rating on a cyberzombie intended for flat-out combat gets pretty sick. Assuming we're talking about the maxed-out human CZ here (-6 Essence), you're looking at a truly silly amount of armor:
12 points of HARDENED armor (absolute value of -6 x 2), +
7-odd points of inherent armor from orthoskin/dermal sheath/bone lacing/carapace leech/whatever, +
Whatever he's wearing OVER it (say, Heavy Military Armor with a helmet and some addons like Gel-Packs and Chemical Seal... not to mention fire resistance, non-conductivity, insulation, etc)... that works out to a 19/17 suit without even having to drag along a shield.
Theoretically, you could get even further out by using cyberlimbs and armoring them, but I've got some issues with the concept of armoring your bones, then amputating those bones to stick on an armored cyberlimb.
I can't think of many automatic weapons in the system capable of taking on a 38/36 armor rating with a 12/12 Hardened Armor core that aren't mounted on vehicles that weigh many tons. Most of the autofire-capable weapons capable of racking up the seriously high DV's run into the 12 Hardened Armor issue... enough successes and you might be able to keep the pre-autofire DV above 12, but any AP is getting wasted on the 25-ish points of armor it hits before it gets down to the Hardened stuff. High-DV small arms might be where it's at... a Panther Assault Cannon only needs to get 3 net successes before its DV gets to 13 and it might at least manage some stun damage if the CZ blows his damage resistance. Missiles would probably work, too. If you're dealing with someone who's not rolling the big -6, the Hardened Armor is less of an issue.
The problem arises when you realize that even if you nail this sucker with an ATGM, you're looking at a possible 50+ dice pool to resist the damage once you figure in remaining Armor, natural Body (maxes at 13 for a human CZ'ed this far out with some genetweaking) and augmented Body (maxes at 19), various 'ware that adds dice vs damage, and all that other good stuff some yahoo thought was a good idea to put into a cyberzombie (like platelet factories, trauma dampers, and other cool implants). You're not going to reliably inflict *any* damage short of hitting it with something that reduces armor by half, rather than a straight -AP, which means you're looking at gauss weapons, lasers, or something with an Elemental effect (and that's where those bonus dice from the armor mods come in handy). Autofire weapons help out a lot here, but the highest man-portable DV you can get with an autofire weapon would be 21+net hits (from the Vindicator minigun), and getting through hardened armor with a base DV of 6 is going to be a pain in the butt. DV's this high, on a bad resistance roll, will add a few points to the condition monitor. CZ's, of course, have a long, long condition monitor (and pretty frequently pain editors).
You could always try modding a Panther for autofire, adding some recoil compensation (gyromount, shock pad and electronic firing gets you 8 points, for a -2 to hit on a 10 round burst... overmodding would let you fit on a heavy barrel for 9 points of RC), and seeing what happens. You could also, of course, just hack him and detonate his cortex bomb