Alright, I did this achievement and wrote down the items as I went. Here is a 100% complete list in order that I found them in the game:
Rebar Bent
Conduit
2x4 Bolt
Large Pipe
Small Pipe
Shovel
Crowbar
Colt .45
Pump Shotgun
Sledgehammer
Mannequin Arm
2x4 Nail
Fire Axe
Taser
Sign
Steam Pipe
Rebar Concrete
Plank
Sawed-off Shotgun
Clothing Rack
Revolver
Locker Door
Gas Pipe (Only a couple in the library level)
Drawer
Paper Cutter
Sub-Machine Gun
Burnt Wood
Desk Top
Rebar
Handrail (Ch. 8 in Yellow Men's Room with Bird #2)
Rifle
Large Plank
Fire Poker
Stick
Burning Wood
Achievement unlocked while I was playing. All-in-all, there are a total of 35 melee weapons.