For me, it's a no. The claw you get is like a weapon: you can use it, but in that case you are not using the tiger claw attack.
As Megistone stated, they are separate options.
Any creature w/ a natural attack who used an attack from a Monk's Stance instead of their own would use the Stance's damage, with zero reference to their own base damage. The inverse is also true.
You'd have two different unarmed attacks, even if they used the same appendage/limb/mouth/etc.
For me, it's a no. The claw you get is like a weapon: you can use it, but in that case you are not using the tiger claw attack.Only thinking they will work together, because the Claws in wild morph
are unarmed attacks.. "These claws are an unarmed attack you’re
trained in and deal 1d6 slashing damage each"tiger Stance is also an unarmed attack.
Think of the stance attacks as separate special weapons, rather than being the same limb doing the damage. Otherwise, all humans would deal Stance attack plus 1d4 for their normal unarmed attack damage.
This extra damage falls easily on the category of "too good to be true".
Wild Morph and Tiger Stance both give a specific attack, not an enhancement to pre-existing attacks. You can't use both at the same time or mix and match their traits and abilities. That would be like staying you're holding a dagger and club in the same hand and dealing both their damage with a single Strike.