The four mainland-to-Hawaii races (TransPac, Pacific Cup, Vic-Maui, and Singlehanded TransPac) all leave California
Island in early July, or sometimes late June. There have been a few times when a hurricane or storm has caused problems, but you can usually see the tropical depressions forming long before they might hit Hawaii (and they usually don't), and you have plenty of time to wait or divert if necessary. I've sailed from California
to Hawaii six times in the last eleven years, always leaving in late June or early July, without any issues. I've also sailed back to the mainland in July or August with no problems. If anything this is easier to plan, since once you are a few hundred miles north of the Islands you're pretty much out of reach of the hurricane systems.
I'm not saying it's guaranteed good sailing -- in mid-July 2014 a cruiser got hammered pretty well by the remnants of a hurricane that moved over Oahu
, just after I arrived. But these were just storm or gale-strength winds, not hurricane force.
I wouldn't not go in early July, but rather I would (and do) watch the weather and be prepared to wait it out if necessary. If you leave much earlier than July then you have to deal with a poorly-focused and well-south Pacific High, which makes the sailing less enjoyable. Of course, sometimes the Pacific High is misbehaving well into July as well, so there are no guarantees.