a brisk trade in AK-47's would develop
Sure, popular gun, available in large numbers (outside most western countries).
How long would it take for them to become commonplace in western countries/Europe?
Hypothetically imagining a trade in AK-47s between Turkey and the UK (around 3,000 km), how quickly could those guns (and ammo) be moved, in enough numbers to be significant? Would the traders be threatened along the way?
Would that trade be on foot (maybe 20-25 km per day), or would they still have the advantage of car/truck/air transport? Would the trade give enough value to account for the traders' risk?
I think that an immediate, catastrophic societal breakdown would give a year or two of extreme regression, during which archery might be useful.
Given a couple of years for the reappearance of traditional techniques (such as hand-crafted blacksmith work) or the redistribution of AKs, things to change.
All that said, it's all guesswork…for all I know, one week without electricity and we could all be Mad-Maxing.
On the one hand, our guesses are based on little except media dystopia fiction like Mad Max and Waterworld, on the other hand, our exposure to those genres could influence our actions to bring about those very outcomes.
So, er, I'm just going to fill up some waterbottles and go stock up on cans of corned beef and archery kit. Although they're definitely not stored at my home, no sirree.