Do you lose the racial stat bonus from the skinwalker change shape ability when under the effect of a ploymorph spell. The obvious answer is yes but the ability doesn't say it is a polymorph effect and the bonus type is racial which makes me think you may not lose it. After all when a elf uses a polymorph spell they don't lose there bonus to dex. It goes with out saying the skinwalker loses all the other benefits of the ability like natural attacks, as they are form dependent.
The skinwalkers shape change is a polymorph effect if I recall correctly. You can only be under the effects of one polymorph effect at a time. So yes, you would have to lose the effects of one to gain the other.
Transmutation
Transmutation spells change the properties of some creature, thing, or condition.
Polymorph: A polymorph spell transforms your physical body to take on the shape of another creature. While these spells make you appear to be the creature, granting you a +10 bonus on Disguise skill checks, they do not grant you all of the abilities and powers of the creature. Each polymorph spell allows you to assume the form of a creature of a specific type, granting you a number of bonuses to your ability scores and a bonus to your natural armor. In addition, each polymorph spell can grant you a number of other benefits, including movement types, resistances, and senses. If the form you choose grants these benefits, or a greater ability of the same type, you gain the listed benefit. If the form grants a lesser ability of the same type, you gain the lesser ability instead. Your base speed changes to match that of the form you assume. If the form grants a swim or burrow speed, you maintain the ability to breathe if you are swimming or burrowing. The DC for any of these abilities equals your DC for the polymorph spell used to change you into that form.
In addition to these benefits, you gain any of the natural attacks of the base creature, including proficiency in those attacks. These attacks are based on your base attack bonus, modified by your Strength or Dexterity as appropriate, and use your Strength modifier for determining damage bonuses.
If a polymorph spell causes you to change size, apply the size modifiers appropriately, changing your armor class, attack bonus, Combat Maneuver Bonus, and Stealth skill modifiers. Your ability scores are not modified by this change unless noted by the spell.
Unless otherwise noted, polymorph spells cannot be used to change into specific individuals. Although many of the fine details can be controlled, your appearance is always that of a generic member of that creature's type. Polymorph spells cannot be used to assume the form of a creature with a template or an advanced version of a creature.
When you cast a polymorph spell that changes you into a creature of the animal, dragon, elemental, magical beast, plant, or vermin type, all of your gear melds into your body. Items that provide constant bonuses and do not need to be activated continue to function while melded in this way (with the exception of armor and shield bonuses, which cease to function). Items that require activation cannot be used while you maintain that form. While in such a form, you cannot cast any spells that require material components (unless you have the Eschew Materials or Natural Spell feat), and can only cast spells with somatic or verbal components if the form you choose has the capability to make such movements or speak, such as a dragon. Other polymorph spells might be subject to this restriction as well, if they change you into a form that is unlike your original form (subject to GM discretion). If your new form does not cause your equipment to meld into your form, the equipment resizes to match your new size.
While under the effects of a polymorph spell, you lose all extraordinary and supernatural abilities that depend on your original form (such as keen senses, scent, and darkvision), as well as any natural attacks and movement types possessed by your original form. You also lose any class features that depend upon form, but those that allow you to add features (such as sorcerers that can grow claws) still function. While most of these should be obvious, the GM is the final arbiter of what abilities depend on form and are lost when a new form is assumed. Your new form might restore a number of these abilities if they are possessed by the new form.
You can only be affected by one polymorph spell at a time. If a new polymorph spell is cast on you (or you activate a polymorph effect, such as wild shape), you can decide whether or not to allow it to affect you, taking the place of the old spell. In addition, other spells that change your size have no effect on you while you are under the effects of a polymorph spell.
If a polymorph spell is cast on a creature that is smaller than Small or larger than Medium, first adjust its ability scores to one of these two sizes using the following table before applying the bonuses granted by the polymorph spell.
I only have access to the ogc so I may be wrong but in the ability it doesn't stat it is a ploymorph effect.
here is the ability in question.
2 claw attacks that each deal 1d4 points of damage
Darkvision to a range of 60 feet.
+1 racial bonus to natural armor.
The racial ability score bonus and additional feature last as long as the skinwalker remains in that form, and a skinwalker can remain in bestial form for as long as she wants. While in bestial form, a skinwalker takes a –4 penalty on Charisma and Charisma-based checks when interacting with humanoids that lack the shapechanger subtype.
A skinwalker can return to her humanoid form as a swift action. To change forms and gain a different benefit, a skinwalker must first return to her humanoid form then use her shapechange ability again. A skinwalker can shapechange into bestial form a number of times per day equal to 3 + 1/2 her character level. Different skinwalker heritages (see Skinwalker Heritages) allow skinwalker characters to select from different sets of bestial features.
The only thing I see that might cause you to lose the bonuses is the line from polymorph about losing form dependent supernatural abilities.
So I suppose the real question is, is change shape a form dependent supernatural ability?
It's definitely supernatural. And I would say that it is form dependent.
As for it not clearly stating whether it's a polymorph affect, consider a regular lycanthrope. The bestiary clearly shows it as a polymorph affect, and skinwalkers and lycanthropes are pretty similar. I think it probably is a polymorph effect, but it doesn't show it clearly.
SQ change shape (human, hybrid, and wolf; polymorph), lycanthropic empathy (wolves and dire wolves)
The abilities are even named the same thing.
Edit: I reread your question and need to amend my answer.
If you talking about the base ability modification to race wouldn't loose that. But, anything you gained from the chnage shape ability you would lose if you polymorphed into something else.
For regular lycanthropes there are ability score bonuses you get in hybrid form, which you would lose if you polymorph into something else. But the base racial bonus to abilities stay constant. I didn't realize that's what you were asking about until I reread the question.
Edit: Rereading the abilities again you're referring to this:
Ability Score Racial Traits: Skinwalkers are well attuned to the natural order of things and value passion above reason. While in their bestial form, they gain a +2 racial bonus to either Strength, Dexterity, or Constitution (see Change Shape). They gain +2 Wisdom, –2 Intelligence, +2 to one physical ability score while shapechanged (1 RP).
So, I'm pretty sure you would definitely lose that, because it's specific to your beast form.