I would do this as a warlock patron: Primal Spirits. Mostly divination and necromancy-related spells, and curses. Archetype features include die-roll manipulation effects, along the lines of divination wizards, Lucky feat, Tides of Chaos, that sort of thing. Plus, communing with spirits and having them go do favors for you. Invocations to match.
And also a pact: Pact of the Cauldron. You can mix potions/poisons and make charms/trinkets. Invocations to match.
...I know you want to avoid direct-damage spells and warlock does have some of these (such as eldritch blast). First, I think that's a mistake: every single class in D&D has some way to dish out severe damage in combat, and your hypothetical new class should, too. Second, I think it's better to just include class features that emphasize non-damaging spells. For example, you could give metamagic-like effects to non-damaging spells, or give some side benefit when they cast a non-damaging spell (maybe temporary hit points or something). This allows players to choose how well they wish to adhere to your vision. The ones that give up direct-damage don't lose as much; the ones that keep a few direct-damage spells aren't getting quite as much use of their class features.
There's some good stuff here. I especially like the Pact of the Cauldron (might be swiping/writing that up just to use with warlocks in general).
The problem here though, as with Elfcrusher's initial proposal, is getting into the situation of wanting 10 pounds of bovine excrement in a haversack with a maximum capacity of 5 pounds.
Is it doable? Sure. If you want to do a whole separate class and break it out into thematic archetype subclasses...you could probably make comparably powered/balanced classes to work in 5e. But a single class (or subclass) with this many bells and whistles just seems overdone/-powered.
If/as a warlock subclass: they are already getting a spell list (and Cap'n Kobold's -I think it was- note about swapping out spells for flavor's sake is well taken, but you also get to dip into other spell lists with the Patron's "Expanded Spells"), the armor and weapon stuff you're looking for, invocations, Patron powers and Pact boons. There only areas for you to play with -for flavor/archetype features- is in the patron powers and the pact boon.
This Pact of the Cauldron seems to handle the "makes charms" area, but it has to be balanced commensurate with the abilities of the existing pacts. Is that going to be "enough" to get across the real desired flavor and abilities here?
Which would leave the Patron ["base class"] features to handle the conjure/contact/control spirits stuff. Easy enough to do, but you really only get, what, 4 features from the base class? 3? Your 1st level power, Pact [Cauldron] Boon @ 3rd, then Patron features at 6th, 10th, 14th. So, 4 abilities/features to cover all communications and abilities with the Spirit World. So, what are those going to be?
The rest is up to the player in invocation and spell selection.
I think there may be room for a whole class with subclasses -this being for homebrew and all. In addition to everything that's been discussed already, I'd think -as shamans are the community's contact and emissary to the spirit world and [may] exert control over them, letting them Turn/Destroy[or at least Rebuke] Undead is yet another feature that seems to be demanded of the base archetype. So now we're getting into mixing and matching Clerical abilities/progression into the balancing mix.
It's a hefty order, but done right, could yield characters for shamans, witch-doctors, fairy tale witches, and what was the last one?
Or go the Warlock subclass way...and while I can see it being a fully functional and easy to whip up character, I don't think it will give you the breadth of characters your OP describes.