Maybe. Depends on how far along the decay is but I don't think it's the skin that's a factor. All bone is held together by ligaments and moved around by muscle and tendons so at some point when his flesh totally decays, sure, he'll just fall apart. Haha.
Most people these days mostly assume a virus is the source of a zombie outbreak but that's relatively a new concept. It was originally a magical source like a ghoul or a mummy so that could easily cause a zombie Logan. Zombies in general don't really make much sense they're fun. Saying a zombie Wolvie doesn't make sense is really just being a party pooper isn't it?