You need to keep your normal skinning knife. You get the bonus to skinning upon equipping the actual knife/sword, but the skinning knife is what allows you to skin.
It drops rarely off the Beast in Upper Blackrock Spire (UBRS). It has a pretty low drop rate... then again your luck may vary. I have done at least 15 UBRS runs, and I have never seen it drop. But as almost every skinner in my guild has one, it is probably just bad luck :-P
I've made a whole lot more than 15 UBRS runs...probably more like 70 and I've never seen it drop.
Zulian Slicer comes from ZG, much more common drop, but unless you're in a guild that's doing it and doing it well, it'll probably be easier to live in UBRS.