Shamans can use two-handed axes and maces in WoW Forever, and Blizzard made it a baseline ability rather than a talent.
They can also use daggers, fist weapons, one-handed axes and maces, and staves. Swords, polearms, wands and ranged weapons are out.
This comes from Forever's own game files: the client's weapon skill table (SkillRaceClassInfo, build 1.60.1) lists which classes can learn each skill. Blizzard hasn't published a weapon table of its own, so we checked the files rather than trusting Classic memories.

| Weapon | Shaman |
|---|---|
| Daggers | Yes |
| Fist weapons | Yes |
| One-handed axes | Yes |
| Two-handed axes | Yes |
| One-handed maces | Yes |
| Two-handed maces | Yes |
| One-handed swords | No |
| Two-handed swords | No |
| Polearms | No |
| Staves | Yes |
| Bows, crossbows, guns | No |
| Thrown | No |
| Wands | No |
You still have to train it
Weapon skills are learned from weapon masters in the capital cities. If something on the Yes list won't equip, train the skill first. Every class is compared in our class weapons guide.
Enhancement wants a two-hander
Blizzard's Shaman post lists two-handed axes and maces as baseline for the class. Dual wield isn't mentioned anywhere, so plan your Enhancement gear around one slow two-handed weapon.
Casters and healers
Elemental and Restoration use a one-hander with a shield or off-hand, or a staff. Pick by Intellect and spell power.
See the Shaman guide, the leveling plan and Shaman totems.
