The Skinning knife has to be equipped to work, but not the BWC.
Research has indicated the following times it won't work.
1. if you have one skinning knife equipped, and have another (or a BWC) in your pack.
2. if you have over 63 items in your pack (including BOD books)
3. if the weight of the leather would put you over 390 (this may be if the weight if the leather as uncut hides would have put you over - never mind the leather never has that stage with the tools)