Yes there are several melee builds that do not use bleeding edge, it's just that those builds deal only 1% of the dps that the BE build can deal.

Which builds for example?
Could you tell me any good skill to build around it?

I would really like to do an assassin/rogue or a tanky warrior.

I suggest to play 1 hand 1 pistol,
at the beggining you struggle a bit, but once you reach lvl 25 this build is a madness.
Dmg you do is insane, and it a lot of utylity - clearing maps with melee is super fast, and your range skills lets you deal with bosses pretty easy once you know the rotation.
Just hit the Fury skills tree along with1 projectile skill, then go for crit tree on the oposite site, -30% dmg with normal hits + 100% dmg with crits.. its insane
you can kill mini bosses just by 1 hitting em with rockets/bombs skills and finish with bleeding edge and some melee attack.
Fun to watch and pretty powerfull.

skill tree so far:
https://wolcen-universe.com/builds/OAew9O-1-hand-1-pistol-so-far

There is a fun (in a sense how 2h melee becomes ranger class) build around Flight of Gaavanir. It's basically a crit build (you can achieve 100% crit chance on that exact skill) which may become shooting skill (with +1 additional hammer from a skill rune and another +1 from ranger passive), or an area damage (if you choose rune to spin hammers on the ground while recalled, requires a bit of mastering to use).
It is not exactly that melee as I would like it to be, but at least it something different to bleeding edge builds.