Bow/crossbow in combination with fel magic, or dual-wielding crossbows with a hatred resource?
The current Demon Hunter already utilizes resources like Pain and Fury. Hatred doesn't seem like that big a leap to me.
Abilities like Strafe also seem pretty similar to what the DH already uses - lots of mobility.
As long as things like the Bolas or Grenade abilities were modified to be "Fel Bolas" or "Hate Grenade" it'd probably work, I think.