I love the extra innate ability we get from using a certain type of weapon. However, the "Spend 1 more AP to deal more damage" kind of stuff is boring and doesn't offer much in terms of strategy and I personally don't even bother using it since the extra damage isn't worth the cost.

Abilities like the shield defensive ability or one-hand with empty off-hand's sucker punch are simply amazing. I don't think I have to explain why.

Here are some suggestions of what I was thinking of for each weapon types:

One hand + Shield
Keep as is.

Melee one hand + Empty off-hand
Keep as is.

Staff
I'd say to keep as is. It's a great innate considering staves are the go-to weapon for a warfare battlemage who wants to beat the ever living crap out of physical warriors and still have tools to deal with enemies that are outside melee range.

Wand + Empty off-hand
Charged shot: 2 Action Point(s) - Overcharge the wand, causing an elemental explosion (Element is tied to the wand's damage type) on impact in a X-foot radius for 1 * weapon damage to all characters around. 4 turns cooldown.

Each elemental explosion would have effects like a wand would. For example: A poison wand would apply poison as well as create a poison surface (or cloud).

I don't think it would feel overpowered considering a bow can use elemental arrows to a similar effect.

Dual wielding melee (Weapons not capable of backstab)
Overpower: 2 Action Point(s) - Strike the target repeatedly with brute force to break their defense. Deal 1 * weapon damage with 25% extra damage to Physical Armor, if there is any. 3 turns cooldown.

Simple but effective.

Dual wielding melee (Weapons capable of backstab)
Feint strike: 2 Action Point(s) - Feint with one weapon, striking the enemy where they are most vulnerable with the other. Deal 1 * weapon damage (Main weapon only), bypassing Physical Armor. 3 turns cooldown.

I know there is already Sawtooth Dagger for Scoundrels, but with two attacks that can bypass Physical Armor, I think it would add to the feeling of being a Scoundrel, using cheap tactics to get past the enemy defense.

Dual wielding wand
Elemental burst: 2 Action Point(s) - Send a flurry of elemental bolts from your wands to overload the enemy magical armor. Deal 1 * weapon damage with 25% extra damage to Magical Armor, if there is any. 3 turns cooldown.

Similar to dual wielding melee, except for casters.

Two-handed melee
Hilt bash: 1 Action Point(s) - Bash the enemy target with the hilt of your weapon, dazing them. Deal 0.5 * weapon damage and reduce the enemy accuracy by 50% for 1 turn(s). 4 turns cooldown.

Pretty self-explanatory. An attack with the hilt of the weapon. It offers that extra attack at only 1 action cost for half damage and an accuracy debuff. This gives a lot of possibilities, especially when combined with the Warlord Talent, when you are missing that extra little attack to get a killing blow.

Bow
Ankle shot: 2 Action Point(s) - Cripple the enemy with a deadly shot. Deal 0.75 * weapon damage, apply cripple for 1 turn. 4 turns cooldown.

The basic "Don't get near me" attack that any ranger should have.

Crossbow
Rapid reload: 1 Action Point(s) - Quickly fire a shot at reduced accuracy. Deal 1 * weapon damage with 30% less accuracy. 4 turns cooldown.

With crossbows costing 3 action points per attack to counter their higher damage, this ability would allow for an extra shot in on a cooldown.