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I lived on Maui in Kihei for over six years. Never camped but hiked up in the Iao Valley, a bit around Haleakala Crater and drove 4x4 around the entire island -some of which is fairly rugged landscape. Iao Valley was quite thick and tropical. An ESEE 4 certainly wouldn't be a bad idea. Better to be prepared for the unexpected. I guess the only caveat would be if you are planning to camp in a very people oriented area where knives may not be welcome. Best of luck on your trip, its a great location! One of the most awesome sights was seeing snow atop Haleakala Crater in Hawaii! It's two miles up though so temperature can dip down.
I also live on Maui, and I would second what mauiblue said.
Also, don't worry about bringing a machete. The only places I ever needed one have always been on private property that I had access to.
Unless you are invited on private trails and hikes, you really don't need much in the way of blades for public hikes on Maui, as they are pretty well established. Its all about water, food, and the right clothes for where you are (wet side/ dry side/ high and low elevations).
Since it is so warm in Hawaii in all the likely paces you will be hiking, fire is a lot less of a necessity. It is really only needed for food and possibly water. Use it sparingly, if at all, as resources are scarce here and there are many protected species.
Enjoy your trip, and remember to take care of the lands and use only what you need. (malama 'aina)
Aloha
-Max
PS- Forgot to recommend a trip to Hana. You'll definitely want to stay overnight. If you can plan for a sunny day in Hana you will have an amazing time. Stay at the camp grounds by the "seven sacred pools" and do the waterfall hike into the mountains. You will never forget it. As long as there aren't clouds out, you'll be able to see the entire milky way in the night sky as well -and from the camp grounds, you can also see the Big Island off in the far distance.