This hidden magic effect is not affected by Blackfathom Sharpening Stone. To make Windfury work in Cat Form, there is a hidden magic effect applied to your attacks. The reason is, that Druids don’t attack with their weapon. This is only true for Druids and not for other classes. The effect of Wild Strikes isn’t shown on your weapon anymore, but you still get the Windfury effect.
Yes, if you apply Blackfathom Sharpening Stone to your weapon you still get the effect of Wild Strikes. Does Blackfathom Sharpening Stone work with Wild Strikes? Depending on your raid composition and gear some consumables might not be needed anymore. It is not always necessary to use it all. The following list of consumables can be brought by Feral Druids to Blackfathom Deeps.