I think that the only real way to get a whole world without guns is to regress to the point where you don't have the means to really make them. Remember that basic gunpowder is not easy to make (the process is complicated), but that the ingredients are not hard to get hold of.
So I can see a few possible contenders for the NOGUNS scenario:
Guns are possible, but they're future-tech
This implies that yes, we can make guns, in theory. However, we don't have the practical means yet. We may not have the population centers to get the division of labour required to kickstart the gun trade, the metallurgy may not be there just yet (and what little good steel you have been able to make is needed right now for other needs, like say, maintaining a large dam that's essential for your agriculture, keeping a bridge up or what have you. This is in my opinion an interesting opportunity because guns are now a possibility, your intrepid rag-tag band of heroes may at some point come into contact with guns, etc.
Guns are possible, but they're unaffordable
This means that there are people with guns, but these people are few and far between, guns are really expensive, and anyone making them without license are clamped down upon. Imagine The King's Guard having rifles, and nobody else. A point to remember here though is that while muskets are not that hard to make, proper modern rifles are impossible without precise machining and measurements. This will give you a setting where there's a reason why there aren't any guns around. Do you want to fight the King's Dragoons riding out to slaughter your entire village because someone went bird-hunting with a shotgun?
Guns are possible, but people don't know how.
Basically, yeah, you come across Hjemmeladeren, an immense bible about loading your own guns. It tells you exactly how to load, what pressures to use for each bullet, etc. If it's about putting gunpowder into a holster and using said powder to propel a small bit of metal into people/animals/others, the book has the best recipe for the purpose. Only problem is, it's in Norwegian, and your society don't read that language. Of course, if you could, you'd know that Raufoss Ammunisjonsfabrikk refers to what's today called Nammo A/S and in your post apocalyptic world would be a smouldering ruin. (Actually, the smouldering is optional.) So even the knowledge you do find is of little use. This would be a temporary solution, so you should set it to happen relatively early after the apocalypse has passed. This also assumes that the sort of people who would know how to make gunpowder from scratch is gone, or if they're still around, are not talking to the heroes. They may in fact be very insular people living in fortified compounds and have little to do with the outside world. (This does give you a Deus Ex Machina if you need it. Chekhov's Prepper Compound?)
Guns are impossible because resource lack
This means that there's none out of one of these:
Because that's how you make blackpowder. It's simply ridiculous. People have also made cannons out of wood and stone. If everyone lives on a boat, then yeah, I can see this being a theme. But if they're on mainland? Can't really see it.
Guns are impossible because laws of physics
I really don't think that this is a good solution. Basically there will be a bunch of unforeseen consequences from this. A lot of unforeseen consequences. If everyone is bigger and stronger? Why do they have horses? How do they get enough food? Etc. I think it's kind of a cop-out.
Guns are impossible, but nobody knows why
At least here you're kinda being honest about it. There's a reason and you totally have that reason planned out, promise bro. But you're not going to tell anyone because it's a plot point. It informs how the story is told, so telling people gives away some of the story. This is a common one to use if you're GM'ing. Just tell them straight up before the game starts that stuff like guns don't work, and that there's a reason for it, but your characters would have no way of knowing that reason. You can admit OOC that it's because it messes with the story you want to tell, but that's fair. Now everyone's on the level.
But for like a written story? It's kind of unfair, I feel. But I'm not the boss of you know, I'm not the boss of you know and I'm not so big~~~
Personally, I'd have to ask myself why I wanted no guns. If I wanted to tell a story with no guns, but would be fine with guns eventually (after the story was conveniently over) reappearing, then any variation of guns being possible but aren't there yet will do the job, and give you more possibilities.
There is however, another question. WHY do people want guns?
Well, guns are really, really really useful. Big guns, such as cannons can hit fortifications further away than catapults etc. can. They're easier to transport. They are easy on your logistics. (You need to bring gunpowder, you don't need a separate team of skilled carpenters to make sure the catapults work.)
If your enemy clumps up, you can smash a lot of them with cannon-fire. If your enemy disperses, you can clump up and smash them. If you're at sea, cannons are simply better than anything else until we get to the modern era. Arquebuses have a longer effective range than bows (as amply demonstrated by the Imjin War), and they're much more deadly, and are harder to armour against. And as armies start to get larger and thus you need to shoot more people, it's important to note the logistical aspects of bows: You need a well trained man, who's trained a lot with a bow, to get an at-all effective archer. You then need to get him arrows. Arrows are large, expensive creatures.
Look at them!
That's a huge piece of wood, and you need to get a good craftsman to make a whole bunch of these suckers.
Meanwhile, an early bullet is just a small lead ball. You also have some gunpowder. Both of these are cheap (lead is inexpensive, steel warheads on arrows are not. Then there's the wood, feather and craftsmanship in addition...), and the package is much smaller than an arrow is per shot. yes, you need wicks for your gunners, if you use that type of firearm. However, bowmen need to have strings for their bows, and crossbowmen need a bunch of tools for their weapon too. It's not a close competition. In addition to that, you don't need as much raw strength to wield a firearm. So your pool of potential recruit is much larger. You can use the big lads to smack your enemies with big sticks instead.
While yes, a well drilled gunner will be much more effective than a relatively fresh recruit, a fresh recruit with a gun will be more effective than a fresh recruit with a bow, all things being equal. (Which they often were not, since a lot of peasant hunted with bows.)
Finally imagine being besieged. You won't be able to get more supplies, so you think yourself lucky that you have gunpowder based weapons, since you can have more ammunition that way. If the enemy brings archers, they cannot engage your gunners, because your gunners can easily stand ready and fire on a moments notice, which the bowmen cannot. In a siege, firearms are ridiculously overpowered.
In other words, as soon as someone manages to figure out how to gun, there will be guns.