As soon as English and French traders showed the native aboriginals in North America (preeminent bushcrafters if there ever was any) what firearms were, those natives did everything they could do to upgrade as fast as possible. The reason for this is that guns, even an old, smoothbore, flintlock trade musket, simply killed better and more efficiently, either for hunting or for fighting, than the bow and arrows produced by a stone age culture.
Hunting is a vital component of real bushcraft, and guns simply do it better. One man here mentioned living off the land with just a shotgun and an air rifle. That is actually an excellent combination when you are operating from a base camp or homestead. A scoped .22LR rifle is also a good tool for the bush (I prefer the Ruger 10/22). A really good, compact gun for the bush, if you have the skill to use it and your laws allow it, is a .22 caliber revolver that has two cylinders, one for .22 WMR and one for .22LR. However, laws aside, it takes a fair degree of skill to use a handgun for anything other than short range defense.
However, if guns aren't your thing for personal or legal reasons, learning other weapons and methods is a must for serious bushcraft.
Here is a YouTube channel that some here might find interesting. He and his people do a lot of bushcraft using the H&R break action, single barrel 12ga shotgun. His video of reloading a 12ga shell on a tree stump with a hatchet and a screwdriver is an example of where he goes with the subject.
http://www.youtube.com/user/wildernessoutfitters
A very interesting video everyone should watch is 'I, Caveman' produced by Morgan Spurlock (of 'Super Size Me' fame). They attempted to recreate, in a valley high in the Rocky Mountains in the USA, a tribe of ice age people using stone tools. They wanted to see if modern humans still had it in them. Much to the shock of the anthropologist watching the experiment from afar, starving and pretty much out of food, they managed to bring down a full grown elk with a dart launched with an atlatl.
On the subject of defense, this is an American perspective, and your island may be a bit tamer, but the world has a bad habit of getting nasty from time to time.
Having grown up in the rural western USA and having spent a lot of time in the wilderness, some of it pretty remote, my personal experience is that self-defense in the bush is an issue. It's been an issue since aboriginal times for all peoples around the world. Archaeologists have found that most neolithic and paleolithic tribes around the world all fought each other on a regular basis. The aboriginal natives of the USA fought each other like cats and dogs long before the Whites arrived. There is a reason that all forest rangers in the USA carry a high capacity semi-auto handgun (typically .40 S&W caliber) and a couple of spare mags loaded with hollowpoints.
This isn't just a modern thing, it has always been like this. The only thing which has changed are the weapons used.
Myself, in addition to the occasional obnoxious human, one of the more unpleasant problems I have had in the American bush is the modern problem of feral dog packs that have no fear of humans. I never go out into the bush unarmed, even if all I have is a blade, like a machete or a kukri. IMHO, you don't need much of what people call 'tactical training' for self-defense out in the bush. If you are a good hunter, alert to your environment, and a good, fast shot, then you can defend yourself if you have the will to do so.