The materials just in the frame of a typical big box store would be sufficient for any basic blacksmith to make millions of spades (and shovels!) using nothing but basic charcoal and a blower.
And you can make several thousand human operated blowers, forges, and small utility buildings also with the materials in a typical big box store’s frame.
The biggest issue would be food and day to day energy requirements and fertilizer. A lot of our economy is highly dependent on refined hydrocarbons and derived products like ammonia/nitrates that aren’t locally producible right now.
For a smith to operate at all there has to be a level of societal stability that could well be too much of a starting assumption in this scenario.
Nah. Smiths literally came along with travelling war parties all the time.
In Europe, nearly every village had one (it was pretty required), and they operated even during active wartime. Because they had too.
All you really need is a skilled blacksmith, a forge, an anvil, and some hand tools. Well, and some fuel and iron.
All that can be transported by cart with a small team of people. In a village, even in wartime, you don’t need to move it, so it’s really just fuel and a few folks + metal feedstock, which is likely even more available from scavenged weapons and the like.