Question regarding Druid Wild Shape & weapon stat damage type

[Sydril]

I recently explored a few builds based on this information from the wiki:

"While in animal form, you will no longer use your equipped weapons for attacking, removing any benefits and drawbacks you would have from attacking with them, but use natural attack "weapons" specific to the form you are in. However you still get most of the additional effects from your equipped weapons:

The ability that determines your attack and damage bonus will be the same as the one used for your equipped weapons. This is especially useful when casting Flame Blade, which uses your Wisdom bonus as attack and damage modifier."

After I respecced my Dwarf to use throw your weight around with axes I realized that the damage from constitution was not being applied in wolf from with an axe of any type equipped, merely the base strength damage. I tried with an unkor's cleaver as well (an axe which has con to hit and damage as an intrinsic property) and still no result.

I then built a purple dragon knight and tested it with charisma and a longsword equipped in wolf form, still nothing, and again with harper int to damage and no effect.

Does anything know if this is WAI or a bug?

*edit* I'd also like to point out that Greater single weapon fighting does not appear to be applying the 1.5 stat multiplier to damage done in wolf form (wild shape)

[lifestaker]

Of note:
animal form uses str for attack and damage, no exception.
Regardless of form of animal, attacks are pulled from Bludgeoning focus/specialization/improved critical.
Weapon type is counted as unarmed for feats and enhancements (important to note unarmed is not a melee weapon.)
Unarmed is counted as THF for glancing blows.
Weapon in main hand will allow you access to select things for spells and enhancements (at least last time I ran a druid):

• Axe = headsman's chop
  Club/quarterstaff = shillelagh

Being it is unarmed fighting many things will not increase your critical range, for they apply to weapon type.
Natural fighting is counted as THF for feats

• Not WAI = open off hand allowing SWF
  WAI = increased 'off hand' attacks for TWF feats.
  WAI = increased AC PRR MRR for Shield Mastery Feats, but not increased double strike or speed if granted by enhancements/feats.

Natural fighting Feats stack 3 times and can be taken with any other fighting style feats.
Armor type still impedes evasion and skill checks while in animal form.