Yes, you're two or three months too early to experience North Shore diving, but maybe you can return to Turtle Bay during the summer months - it's only 20-minutes away from the best NS sites, so there's no better place to stay, in that regard! - and check it out. It's absolutely lovely.
Diving on Oahu during the winter months is confined to the south and leeward (west) coasts of the island.
ChimChim75 is spot-on... I wouldn't recommend certain South Shore shore-diving sites unless you've either done them before several times and know exactly what to expect, or have a knowledgable local guide. That's because some south shore sites like Lanai Lookout and China Wall involve a bit of a scramble up and down rocks/cliffs, so just getting in and climbing out can be an ordeal for the out-of-shape, especially since one is obviously in full gear. It also takes an experienced eye to know when the sites are divable, and to advise you on the entry and exit points. Electric Beach is a fairly simple shore-dive site on the leeward side, but I suggest speaking to a local dive shop before you do so - not only so they can provide you with tanks and weights, but also to confirm that the water's behaving itself. Usually, the leeward side provides the most reliably good diving conditions year-round, but like all stretches of water, it has its off days.
There's no shortage of dive shops on Oahu that can take you boat diving - some also offer night diving once a week or so - and they will pick you up and drop you off in Waikiki. Once again, the bulk of your diving will take place on the South Side (perhaps out of Hawaii Kai) or the leeward side (out of Waianae). You can also meet up at the boat or at the dive shop, if you prefer. Not sure about a Turtle Bay pickup, though!
So, yes, bring your gear, get wet, and maybe you'll get really lucky and spend your dive listening to whale song. They should be around for a little while longer, and you won't want to miss them !