The only actual skill of value in a post apocalypse scenario is convincing people around you to not murder you for your meager possessions. Humanity without a state has no qualms about murdering a member of an out group, and it can even be a bonding activity for the in group.

Left to our own devices we form tight knit, small scale communities which are very protective of each other but extremely hostile to anything else. There's no "society", no "technology", no "time to build something". Look at the Primitive Technology guy on youtube; Even very basic metal is impossible without industry, so no metal ax, no metal parts for anything. Stone tools are incredibly inferior to even basic modern tools.

The spare people and time required to develop and work an industry to start building ANYTHING more than a weaved basket or stone ax requires the recreation of agriculture, except nearly none of the survivors of any situation will understand anything about growing plants, and we don't have a hundred thousand years of human history practicing while being nomadic hunters.

Your gun won't protect you. Your stores of food will run out. Your knowledge of anything that isn't "how do I sustainably produce one million calories a year with only my bare hands" is useless.