Try giving either Ocean Concepts or Island Divers a call - they both have websites. I belong to both their dive clubs and dive with them often.
Ocean Concepts dives mainly out of Waianae on the west shore, but near the end of the year they do more dives on the south shore.
Island Divers primarily operates out of the south and east shores.
Both offer shuttle service from Waikiki. Your best bet is to dive off the south and east shores that time of year - there are lots of wrecks to choose from. The YO-257, San Pedro and Sea Tiger are popular wrecks off the south shore. The Corsair is the most popular wreck off the east. There are some less visited barges off that side, also.
As far as weather - if you're talking about rain - they'll still go. If you're talking about surf or sea conditions, they'll make that decision as they assess the conditions that day. I've never had a dive called for inclement weather (we just really don't get much of that) and very rarely is the dive called for sea conditions. More likely they'll just choose another site.