I got asked this question recently, and RAW nothing seems to be in conflict. Although I have some doubts about the other feats in the chain (Crane Wing & Crane Riposte). So, can Crane Style be used while in Wild Shape?
1 Answer
Yes
A druid retains his feats while in wild shape; nothing about style feats in general, or about Crane Style specifically, changes this.
In fact, Crane Wing and Crane Riposte can be used too—but the “free hand” requirement is a bit of a difficulty. If you wild shape into a form that has hands—a primate, usually—then you should be able to use these feats. Otherwise, probably not, though personally I find no reason players in my games shouldn’t be able to hold a claw or similar in reserve (i.e. not use it when attacking) in order to benefit from those feats.
Of course, I would also warn players in my games that all three of these feats are quite poor, and recommend they reconsider taking them at all.