You are going to have to come up with houserules galore to make this work, and in general it's a bad idea. Here's some of the major points you're going to have to hit:
Damage Reduction has to be changed
Anything with DR/Magic will have to be changed, as this party can't overcome magic DR without magic weapons. If you can't overcome it, everything with it gets a LOT tougher. Ditto for DR/Good, or any other type that requires magic items or spells. Cold Iron and Silver are okay still.
Challenge Ratings will be Way Off
At low level, CRs will probably be pretty reasonable. As you go up in levels however they assume both access to magic items and to magic. For some monsters that won't be a huge deal, and you could just level adjust them.
Think about a Dragon. Any smart dragon is going to fly around above the party and simply breath weapon them to death, because a team of fighters without magic items really can't do a whole lot that's meaningful against a flying dragon. Dropping the CR by 1 or 2 won't make a lot of difference. Bows are simply not scary to dragons (particularly ones with damage reduction).
Then there's stuff like the Night Hag. More DR to change/remove. It can cast invisibility, which the party can do nothing about. It can cast Deep Slumber, and given a party of Fighters will likely all have base poor Will saves... that's a bad day.
Oh yeah, and it can turn ethereal, dream haunt, and shoot strength damaging rays. That's a bad day, though at least in Pathfinder the ray doesn't stack with itself. God forbid they come up against one of the nastier undead with high HP and a lot of magic abilities.
You see the problem here? The party has no energy damage defenses, no turn undead, no freedom of movement, and none of the other defenses that let a party survive against the more dangerous stuff.
Tweaking CRs won't matter. When you get to higher level, you're going to have to either significantly rewrite, or simply throw out large sections of the monster list as totally unusable.
What do they Spend Money On?
Oh yeah, loot. What are you going to give them? Magic items comprise most of the loot in the game, and as you noted are necessary to continue to progress stats like AC. What are you going to replace that with?
If the answer is nothing, the party is going to wind up with nothing to spend money on very quickly. So you're either going to have to bring magic armor back, or create a functionally similar equivalent that does the same thing only isn't magic... which is just semantics at that point anyway. Maybe a "super Masterwork" or something.
If you don't, then after a couple of levels there will be no items left to give out that they'll find useful.
You mentioned trying to fix the armor problem above with feats. The problem with that is that those feats will be mandatory. Anybody who doesn't take enough Dex to pick up Dodge will be in a world of hurt later if Dodge is one of the only scaling ways to boost your AC later in the game.
So if you do make some feats have scaling armor bonuses, people will have to take them. That's going to make every character pretty much identical in feat selection, because they have no choice if they want to get more AC and thus survive.
How do they Recover After Combat?
You noted this problem already. The normal rules for this will be unworkable fairly quickly, unless you want to just do one fight a week. The simplest houserule is to allow Heal to fully recover HP after a couple hours out of combat.
Don't Do This
I could go on, because there's more problems than the ones I listed. But really... don't do this. You're trying to use the system opposite the way it was designed to be used, and the system doesn't like it. Magic items are so baked in that you can't remove them. At best, you'd have to replace them with non-magic equivalents, at which point you're not actually accomplishing a whole lot. The entire game is balanced around these things existing.
If you don't replace the magic items with functional equivalents, you'll have to throw out a huge pile of monsters because the party simply can't fight them. You'll have to rework mechanics, alter rules, figure out what in the world to give out for loot past level 3, and effectively be making so many changes that you're now playing your own system and not Pathfinder.
Alternative - Low Magic Game
What you could do is a low magic game. That is, nobody is allowed to play full spellcasters (Wizard, Cleric, Druid, etc, but Paladins and Rangers are in), and magic items are rarer or harder to create than usual (we had around 50% normal wealth for our level). In that case the party has less access to spells and magic items, but can still get them. If you do that, you can get by using monsters with lower CRs, and the list of stuff you just can't use is much, much smaller. The party still has items to buy and loot to find, and when +2 flaming magic swords are rare, finding one is a big deal.
I've played in a game like that, and it can work fairly well. The DM has to be on the ball about monster selection and encounter design of course, and the party has to choose how to spend their more limited magic item wealth very carefully. But the game still works, and it gets the feel you're looking for.
If you really, really want a no-magic game, I can't recommend strongly enough that you pick a different system. One designed for that, and there's lots of them. That would be another question, with the system recommendation tag.