I found buying the original classic controller pro by Nintendo was best. I have not purchased 3rd party classic controller (only the pro). It is not a matter of whether they work with WODE or not more so the wii games.
I had a classic controller pro (3rd party) and it worked fine with wii games but with HomeBrew it had major lag. After the dev updated the HomeBrew app it worked a lot better but not perfect.
I then purchased an original pro and had no issues with HomeBrew or wii games.
Sometimes it is best to pay a little more to be hassle free.
P.s. the pro is much more comfortable to hold than just the classic however, not 100% sure of the pro works with all wii games that want the classic... Never tested. I only ever got the classic to play HomeBrew an dthen found I liked the pro better
never wanted them to pay original wii games...