Hey everyone!
I’m new here, this is my first post so I hope this is the right thread for this.
I want to make a 2H melee build, but don’t want to use soldier for cadence, shaman for savagery or demolitionist for fire strike. Can I make a build, that hit hard enough without these to complete the story? (I’m not interested for endgame yet)
Hi Pulcsy and welcome to the forums 
It is certainly harder to create a melee class that doesn’t use a default attack replacer, but it is by no means impossible, especially if all you want is to clear normal. Out of curiosity, what class combo and damage type are you looking at that doesn’t include one of the 3 classes with attack replacers? I have a pretty badass 2h acid witch hunter that doesn’t use an attack replacer but it is more of a caster than anything because it relies on ring of steel, shadow strike, and Amarasta’s blade burst (which is debatably an attack replacer anyway)
Generally it is beneficial to have a default attack skill for melee, if you are a pure-weapon focus.
Some items and components do provide such a skill, even if a class has none. One example of this would be the component “Shard of Beronath”, which has lvl 55 restrictions.
You may need an alternate killing method (ie. spells) until you get to the required level. Depending on your mastery choice, you may even find that this alternate killing method is better than any potential default melee attack.
As said above, you should specify a mastery of interest for further community recommendations.
(OR you can search the Grimtools item database to see if there is an attack-replacer of interest.)
I wanted to do a aether based build, but in the devotions I saw it’s usually come with lightning, so I choose Necro and Shaman, but when I searched for a weapon or other gear, a lot of the aether dmg came with Arcanist and the +to skills as well. That was the thought process. But I’m not sure how much I can rely on legendary gear, while playing the story, so maybe that would answer my question 
Welcome to the forum.
Depends on what you mean by main attack. Do you mean just those skills that are auto attack replacers like Cadence, Fire Strike and Savagery? Or do you mean any skill that could be put on the LMB? If the first then there’s Amarasta’s Blood Burst as mentioned and also Shaman’s Primal Strike as well as components which give similar skills which you could use.
If you mean the latter then it should be possible, but will probably be much harder to win fights with.
Necro/Shaman is usually a pets class I think. I’ve never made one myself so I don’t know all the options, but skeletons are strong in the campaign. Necromancer can be good for Aether melee, but it is usually paired with Soldier and uses cadence.