There are lots of people who sincerely believe they can sail around the entire globe with nothing more than a sextant and some old, outdated charts. Yep, you can do it, and some folks actually get away with it. Some don't! Yeah, being a traditionalist may be OK for a miniscule number of boating enthusiasts, but for the most part, being a traditionalist doesn't really make you a better sailor/boater - it just makes you a traditionalist.
From my perspective, cruising, whether around the globe, or just around the lake, or Chesapeake Bay, is something that need not be a dangerous challenge. Those electronic goodies make life a lot easier, provide you with all the bells and whistles to make cruising a lot safer, and allow you to CRUISE! Maybe I'm lazy, but I really don't want to work at cruising. I want to sit back, relax, set the sails and enjoy the ride. I want to watch those American eagles swooping down and grabbing fish from the surface of the bay, shoot photos of the action, and not have to worry if the boat is going to run aground. If the water gets too shallow, that depth alarm will let me know in short order.
I want to cruise over the reef and watch the sail's shadow on the coral below, knowing with a quick glance at the GPS/Plotter/Depth finder that the actual depth is much deeper than it appears.
I really enjoy cruising at night under a beautiful array of stars and not worrying about unseen objects floating in the surface of the water that any HD-3G Radar system can easily detect and provide an audible alarm. I want that freighter coming up the channel to know I'm out there too, even if they can't see my radar reflector. That AIS system could be a life saver.
That said, I've DR'd back to an inlet in a driving thunderstorm packing 55 MPH winds while dodging sheets of lightning. It was scary as hell. This was pre-GPS/Plotter, a time when Loran-C was the best electronic navigational tool available. They just didn't function in a thunderstorm because they operated on the AM frequency bands. I was fortunate. I came in about three miles north of Chincoteague Inlet, decided to turn left, and get real lucky. The inlet, which was barely visible in the storm, was experiencing a hard, ebb tide, and the winds were blasting from the northeast, thus the standing wave, which is normally only a few feet, was nearly 10-feet high. I was in an 18-foot powerboat and was able to blast through the wave and take shelter inside Chincoteague Bay. If GPS/Plotters were available back then, I wouldn't have wasted time looking for the inlet and would have beat the worst of the storm and have been in the bay by the time the storm hit.
So, if the officials won't allow you to leave New Zealand for that world cruise, I guess you have a couple options. You could sneak out of the harbor one night, under the cloak of darkness, and maybe, just maybe, you might successfully circumnavigate the globe and make it back alive. Then again, you just might not. Or, you could take what's behind door number 2, upgrade the boat's navigation and safety gear, leave the harbor in broad daylight, prop your feet up and circumnavigate the globe knowing exactly, within a few yards, where you are during the entire voyage - day or night, stormy skies or clear.
Sorry about the rant,