If I didn't have free reign of choice, I'd take a sharpened military spade [aka, the Lobotomizer] that could be fixed on either a polearm-length shaft or a single hand shaft. Doesn't take much effort for this to split a skull in half and scoop out a brain [see Deadliest Warrior: Green Beret vs Spetznaz episode]. It's light, versatile, sturdy, simple, and doesn't need to be sharpened all the time to be effective like a katana.
If I had more flexible choices, I'd go with a Spartan Aspis (shield) forged with modern metallurgy for increased durability and lighter weight. Covers basically your entire front, keeps you away from those infectious teeth, and definitely has enough mass to send a zed-head flying. Edged strikes a la Captain America pack more than enough force to destroy the brain. Of course, this isn't even an intended weapon so you can still pack a primary. Pair this with a yari or iklwa on a javelin length shaft to complete the set.
Or go with a pair of armored katars. The speed of a punch dagger combined with the armor-piercing strength of a pike. Kill zombies as fast as you can punch them.
If I didn't care to go quietly: the AA-12. It has low recoil, minimal to no maintenance required, and is sturdy. Choice of 8, 20, & 32 round magazines with a wide range of 12-gauge specialized ammunition. Fin stabilized Frag-12 & HE-12 slugs can reach out to 175 meters and pack enough firepower to turn the AA-12 into a mini-grenade machine gun that could shred vehicles [aka: the Bolter]. Of course, I'm not ever gonna go full-auto since that's just a stupid waste of good ammo. Also, regular 12-gauge ammo is plentiful thanks to its popularity in the hunting community.
