Yes, islands and other highly-defensible areas can be held using a navy. But hiding on an island is different to actually going out and holding land. Tactically, an island fortress is just the same as a big, stationary ship.
It's not just the weapon, it's how it's used. Have you seen a Khanda in action? There aren't really any good videos to justify it, most of them show ritualised demonstrations and dances. Western swordsmen parry, cut and stab. A Khanda spins like a propeller blade. It's much heavier than a western 1-handed sword (more like an axe) and can knock away anything it comes against. The closest western equivalent is one of those fantasy ball-and-chain weapons. And the same patterns of movement can be applied to different weapons for different effects. Axes, maces, chain-shields, flexible, 3-foot-long serrated swords. British soldiers in the Punjab campaigns reported that enemy troops would keep on attacking even after being transfixed on bayonets.
I will admit that by the time we went to India the fully armoured infantry with broadsword and shield was considered mostly obsolete. British military doctrine had moved away from close combat, and had moved to focus on rifles or musket and bayonets. That said, officers were still expected to be familiar with swords, but as a ritualised dueling weapon. This is in the same way that mostly naked Zulus were able to use spears to stab a large number of British soldiers, armed with the latest in firearms technology, to death in Africa. I hope you aren't intending to argue that they were on a par militarily with the British Empire of the time?
However: the "fantasy ball and chain weapon" you refer to is called a flail. It is real, and sometimes confused with the morning star - as far as the information I have seen this is a spiked mace.
In addition, if you can funnel more men with weapons at a block of riflemen than they can cut down with bullets in the time it takes you to get to them, then you have as advantage. Rifles or musket with bayonets are not ideal melee weapons, especially against any decent practical melee weapon. Hell, even a decent greek pike block could crush their way through a musket line if they got to it intact.
Spinning your weapon like a propellor is not an efficient way to fight. It uses energy and tires you. It commits you to a fixed pattern of blows.
I would be interested to know what European one handed sword you are comparing the khanda to as well. Was it the cinqueda? Was it the rapier, the small sword, the backsword? Was it English or Scottish broadsword? Could it perhaps be one of the many court swords, or the sabre? Perhaps you mean to compare it to the cutlass or the bastard sword, used in either one or two hands, depending on what else you are using, and the blows you are employing? All of these are very different weapons, and used in different ways. The bastard sword can be used in such a way that you weave a figure eight pattern, but although it is great at encouraging people not to approach or step into your reach, if it is parried or stopped it leaves you vulnerable whilst you switch to actually placing blows that are aimed at something. As I say though, these were considered obsolete.
Perhaps this would be best dealt with by something akin to the fire/shock system that exists. Rifle units get good fire and poor-moderate shock (melee phase). Khanda armed troops (or earlier European broadsword troops) would get no fire, but good shock.
As for being transfixed on bayonets, you get stories of people being shot through with modern assault weaponry and it not stopping them dead. If it's just gone through muscle tissue rather than hit vital organs the adrenaline can keep going for minutes afterwards. If it's "just" a gut wound, people can live for weeks afterwards, before dying of infections. They can even recover. In a fight, just because someone has had an arm smashed and mangled doesn't mean they can't still stab you as well. Just because they've got a 1 inch wide hole in their left shoulder doesn't stop them stabbing you with their right.
