It really needs to be said here that all of this is much, much easier and faster to do in TES5edit than in the CK, and there is no 1st person bug in the former. TES5edit puts all the resources by mod, alphabetically by resource type under the mod, then individual resources within the type's section arranged by FormID (arrangement of specific records within each resource is a bit less user-friendly, but is consistent between mods). This makes it very easy to find stuff, especially given the table-sorting feature (by column), plus search (which works as a "find it in the list" not the CK's "make everything else invisible" behavior). You can duplicate a resource with a right-click option, and easily rename things. When you change the ID of something, TES5edit updates all references to it in other records automatically.
To re-texture something in TES5edit:
* Start TES5edit, which fires up about 10x faster than the CK, and does not load a bunch of Steam junk into memory. Right click in the list and pick "Select none", then select the specific mod(s) you want to work with (put a checkmark next to it).
* Create a new Texture Set record (or copy and modify an existing one), in the current mod you're working on or a new one, as you like/need. (Right click the resource in the original mod, in the left pane, and pick either "Copy as new record into ..." or "Copy as override into ...", rename the Editor ID as prompted, and either pick your existing new mod you're working on, or the option to create a new one).
* Adjust the texture paths to what is needed for that retex. If any record type you need is greyed out, then right-click it and pick Add. To edit the data in a specific record, right-click and pick Edit - or slow-left-click it twice and wait a second for the field to become editable. This applies to pretty much everything in TES5edit's right pane.
* Copy the Armor Addon record you want to retexture as a new record into your mod (if it's an add-on) or as an override (if you're doing a replacer), and right below its male and/or female world model (biped mesh - some items have both, some have just one if they're female-only or whatever), you point its Alternative Textures record at the new Texture Set's ID (and set the proper "3D name", i.e. NiTriShape or NiTriStrip ID from NIFskope). If it has no such record yet (greyed out), right-click and pick "Add" to create the record type, then do it again to create the specific record, the Edit to edit it. Complicated items with multiple NiTri[whatever]s that you are changing the texture of will need one of these for each node you are changing. Really complex ones may even use multiple separate texture file sets, e.g. a set of metal parts for the armor and another set of cloth textures for an underlying shirt below the metal parts. The item is going to need one Alternative Textures pointer to a Texture Set record per NiTri[whatever], even if you only changed one of them with something custom.
* Repeat this Alternative Textures pathing process for the 1st-person mesh if it has one (typical with gauntlets/gloves and long sleeves on a cuirass/robe).
* Copy the Armor (item) record so you have added your new item, and point this at your new Armor Addon record as the armature to use. If it has a unique ground mesh texture, then point that one's alternative texture record to the same retex (or to a specific file or set of files if the ground mesh has separate ones, e.g. for a silly gift box instead of the armor folded on the ground). If you're just doing a replacer, then you won't have to do all of that, just change the extant item's ground mesh to point to your alternative texture set.
* It's basically the same for weapons, except you need to edit a Static (1st person) and Weapon record instead of an Armor Addon and Armor record. Depending on the item, you may have separate meshes for 1st-person, right, left, and sheathed, on a per-weapon basis. As far as I can tell so far, as long as you have a 1st-person Static record, the game should load these automatically and apply the same Texture Set (kind of how it does with the *_0.nif version of armor items specified in the ESP with paths that end in a *_1.nif filename).
* When done texturificating, close TES5edit, which will prompt to save the changed mod (and will auto-create a backup copy before it does so).
That's all there is to it. You can do in 3 minutes in TES5edit what could take 15 minutes or longer in the CK. The time savings are massive when you're doing a bunch of retextures, since you can block-copy entire sets of gear, and there are TES5edit add-on scripts for doing things like batch changing of texture paths.
The only tedious thing (and it's still less tedious than in the CK) is if you are block duplicating a whole bunch of stuff (like making a silver armor set also available in 5 other colors), you need to duplicate a bunch of Texture Set, Armor Addon, Armor, and (if applicable) Constructible Object records (and possibly others, if fancy stuff is going on like different enchantment spells and magic effects for each recolor). If you're doing this between mods this temporarily makes the original mod a master. You then have to go down the list and customize the Texture Sets, point the new Armor Addons at them correctly, update your new Armors to use the new Armor Addons and new ground-mesh Texture Sets, then point all the Constructible Items at the correct new Armors, all by ID. After this is done, remove the original mod as a master of your new mod (in the File Header record), then do right-click on your new mod's name in left pane, and run "Check for errors" to make sure you didn't miss any IDs you needed to change. (If you're retexturing something vanilla from Skyrim.esm, or from a DLC that your mod will permanently have as a master for some other reason, you have to be more careful, since you can't remove such masters without breaking your mod, and thus have to double-check record by record that you've used the proper new-record IDs and not left copied ones in place from the original resources you're trying to re-texture).
The only frustrating limitations of TES5edit for typical/basic modding are that it doesn't have a renderer (you need to use the CK, the game itself, or some third-party tool like NIFskope or Outfit Studio (with texture paths set up right) to view the item visually; and it doesn't have a script editor/compiler, so the Virtual Machine Adapter record group cannot be created in TES5Edit, and parts of it cannot be edited (though can be deleted). It also doesn't have audio editing and various other stuff which most people don't need. And it can't do the head exporting that CK does to make modified NPC faces actually show up in-game. So, you can't throw the CK away. >;-) TES5edit is mainly intended for cleaning/fixing mods, and doing non-audiovisual editing of mod data, and it truly excels at these things.
PS: It helps to pay attention to what things use the same IDs and paths and such, so you can make use of easy copy-paste from one resource to the next one. E.g., it's often better to do all the red gear, then all the blue, etc., than to do all the cuirasses then all the gauntlets, because all the red gear is likely sharing at least some texture files and will need to renamed to have consistent in-game names (and at very least, you keep them grouped and easy to keep track of). If all the gear of the same item type also shares some textures file (e.g. normal map), if you use an Editor ID naming pattern like MyModderHandle_ArmorName_Curiass_Blue, you can then sort by Editor ID and get all the variant-color cuirasses grouped for easy pasting, one resource after the other. Similarly, it's better to do the crafting recipe resource and the tempering resource for each item, then the next item, than to do all the crafting recipes then all the tempering, because both types of Constructible Object resource for each item are going to want the same item ID to indicate the resulting gear item that the smithing produces.