The Av Melacha-Shearing wool from skin:
One who shears hair or wool from a living or dead animal, whether the animal is domestic or wild, or even [if he shears wool/hair] from removed skin, he is liable [for a sin offering]. Doing so is amongst the principle Shabbos Melachas as in the Tabernacle they would shear the skin of the Techashim and rams.
Using one’s hands to remove the wool:
One who removes wool with his hand from an animal or from its skin is exempt [from a sin offering] as this is not the common form of shearing. [However it is Rabbinically forbidden as will be explained next]
Summary- Shearing hair/wool:
Using a Vessel: It is a Biblical prohibition to shear hair/wool using a vessel, whether from alive or dead animal, whether from a domestic and wild animal, even from removed skin. Doing so is amongst the principle Shabbos Melachas as in the Tabernacle they would shear the skin of the Techashim and rams.
Using ones hands: It is Rabbinically forbidden to remove wool with one’s hand.
May one pluck a feather from his piece of chicken?
This matter is disputed amongst Poskim. The dispute applies even if one intends to eat the chicken right away after removing the feathers, due to a question of whether this involves the “Shearing” prohibition. Practically one should initially avoid removing feathers from chicken, [although those that do so have upon whom to rely if they eat the chicken right away]. This prohibition certainly applies if one desires to remove the feathers in order to make the chicken more presentable to the guests in which case one must take great care not to remove those feathers.
For later use: According to all it is forbidden to remove the feathers for later use due to the Borer restrictions.
 Shabbos Kihalacha Vol. 2 p. 229
 The stringent opinion: Is brought in Ketzos Hashulchan 143 footnote 1 in name of the Yeshuos Chachma, and so plainly rules SSH”K 3/30.
The lenient opinions: The Ketzos Hashulchan [ibid] himself says that the world is not accustomed to be stringent in this and he goes on to be Melamed Zechus through four different reasons for why removing feathers of cooked chicken does not contain a prohibition of “Shearing”, and he thus concludes that one should “leave the Jews to do so”. So rules also that it is allowed: Shut Har Tzevi, Yalkut Yosef, Igros Moshe.
 So rules Rav Farkash ibid, however the Ketzos Hashulchan rules that the world is lenient in this, and so rules Piskeiy Teshuvos [340/2].
 Ketzos Hashulchan 143 footnote 1
 As this is similar to the removing of the skin or peal of a fruit which is only allowed to be done prior to the meal. [Piskeiy Teshuvos 340/2]