Javascript (ES6), <strike>84</strike> <strike>80</strike> 78 bytes
-

 i=>new Set(s=[...i]).size>2?[i,s.reverse().join``].indexOf(s.sort().join``):-1

Where wavy increasing is 0, decreasing is 1, and -1 is not wavy.

Thanks to [@Neil](https://codegolf.stackexchange.com/users/17602/neil) for helping me save 2 bytes.