Well, the existence of zombies wouldn't make things suddenly stop working. More than likely most steel mills would be "operational" but as you said, the average person couldn't run one.
However there may be stockpiles of gun parts at weapon manufacturers, and simpler components could be created at a machine shop.
I agree on this point, some industrial sites and almost all tool shops and fabrication shops would be good to go for several years after the event, as long as water doesn't get in and rats don't chew cables or something.
So for most machines all you would need is a mid-sized 3 faze generator. (for laths, drill presses, mills, grinders, plasma cutters etc.)
Bigger machines like a CNC would need a large full sized generator. ( A CNC is a machines that can be programed to cut blocks and sheets of metal into different parts, like a gearbox sprocket or a gun receiver)
And then tools like oxy acetylene torches would run without power as long as you have fuel and a way to light it. They could be used for welding and cutting basic stuff.