Hmmm, in Shadowrun this would not be a kosher combination, but if you could convince your GM to allow a lot of house rules in the name of fun, then go for it

According to normal rules though:
A) Shapeshifters are magical creatures. There is no technological way to change into another animal form and back. It's magic all the way.
B) Shapeshifters are limited to one animal type...actually to be more correct, Shapeshifter animals are limited to one
humanoid type, as the default form of the Shapeshifter is of the specific animal, not the humanoid.
C) If you want to be a humanoid with a choice of Animal shapes, the Shapechange spell is your best option. However it requires you to be a full mage, which conflicts with your '
no magic' requirement.
Again, according to normal rules, here is what I think your options are for a Physically based character who mimics animal powers:
1)
Physical Adept: Magic based who funnels magic into physical abilities (Stronger, better, Faster etc). This allows you to agment your abilities along a tribal theme, and you can rationalise these abilities however you like: '
Eyes of the Hawk, Strength of the Bear, Ears of the Wolf, Speed of the Puma' is a term that comes to mind.... a cookie for anyone who gets the reference

However, this won't allow any full shapechanging into an animal type, unless you are a Shapeshifter Race (as per option A) above
2)
Technical augmentations: Similar to option 1) but technology (Cyber ware, bioware, genetic customisation etc) can give you animal-like powers. These are harder to thamatically rationalise though, as technology is inherently static. Getting your abilities from a pair of
Zeiss-Mk3 Cyber eyes, doesn't sound particularly animalistic...
3)
Mage: With a clever combination of attributes and powers, you could be a humanoid mage (as per option C) who casts the
Shapechange spell as needed to: Fly away as a hawk, attack as a bear, sniff around as a wolf, etc etc
Also, the big thing about myths in Shadowrun is that many of them have come true via magic. I don't know what skinwalker myths you may have that
don't involve something supernatural? o.O
What you should go for is entirely up to you. I hope this stuff helps

Cheers!