The Armorist's spellcasting is about half the class's power, and removing it would heavily nerf the class. If you strip it away, the only ability of note that the class gets is saving some money on magic items. (On paper, it also has its armorist tricks, but they're really just there to let you customise the magic item summoning a bit and don't add anything much of their own. They're not in any way comparable to, say, a fighter's bonus feats.)
As it happens, there's a precedent for the power of classes that just give you magic items: the 3.5e Soulknife, widely considered one of the worst classes in the system. When Dreamscarred Press updated the Soulknife to Pathfinder and made it decent, a large part of what they did was giving the class combat abilities besides the magic item itself. Now, this hypothetical Armorist wouldn't be quite as bad as that (he can, at least, summon armour too, and has a bit more choice about what enchantments to give his items) but it would still be very poor.
Fortunately, there's a conversion we can do to see how much the spellcasting is "worth" in terms of first party content. It's a bit rough around the edges, and uses a couple of different mechanics, but it's good enough for a ballpark estimate of what you ought to replace it with.
The Spheres of Might rules (written later, by the same authors) allow you to trade out a Low spellcasting progression like the Armorist's for a Proficient martial talent progression:
Some classes who naturally combine martial prowess with spellcasting,
such as the inquisitor, paladin, and ranger, can choose to opt to
replace their spellcasting progression with a combat training
progression. Classes whose maximum spell level would be 4 (or Low
Casters if using Spheres of Power) may exchange their spellcasting for
the Proficient combat training progression...
As you can see from the above quote, you can also replace the casting of a 4-level-spellcasting with that same Proficient combat progression. It therefore seems reasonable to replace the Armorist's spellcasting progression with 4-level spellcasting from whichever spell list seems to fit the flavour of the character best. Paladin, perhaps? My gut feeling is that 4-level casting from Paizo is actually a bit weaker than Spheres Low casting so this would still be a bit on the weak side, but it would at least be reasonably playable.
Alternatively, if you don't want to give the class any other magic at all, there's another exchange that we could reverse engineer: instead of giving up their spellcasting, characters can give up their 1st, 5th, 9th, 13th and 17th level bonus feats from character level in return for a Proficient progression, an exchange that's sort of similar to variant multiclassing. Thus, a bonus feat at each of those levels might be a reasonable exchange for the loss of the casting. I'm a bit dubious about that, though, since giving up five of your ten bonus feats hurts a good deal more than gaining 5 extra ones helps you. It might be worth adding a little more on top of that.