The recent discussion about hooks and ropes have suddenly made me realize that in 4D, swordfighting is ... basically impossible, except in a very strangely modified form (which is totally impractical in a real fight).
The bottom line is this: for maximum maneuverability, 4D swords will have to be essentially 1D sticks (well, slightly widened and sharpened for piercing, of course). But due to the extra dimension, this means that it's basically impossible to parry. Trying to block an incoming 4D sword blow with another 4D sword is like trying to shoot down a bullet in midair -- it's so unlikely that it's essentially impossible.
Also, 4D shields will need a 3D surface area in order to stand any chance of blocking an incoming 1D sword blow. Even if your shield is extended in 2 dimensions, trying to block a 4D sword with it is like trying to block a bullet with a stick in the 3D world. It's a little more likely than shooting down a bullet in midair, but still so unlikely that it's just not practical in any real sense. This means that shields are bulky and cumbersome in 4D.
The only thing that remotely resembles parrying in 4D would be if both combatants wield weapons that are extended in 2 dimensions. Such things act as intermediates between swords and shields: you can still cut with the 2D "swordshield", and you can also parry your opponent's swordshield blows. But if your opponent wields a 1D sword, then you're out of luck: your "swordshield" is pretty much defenseless against it. Plus, a 2D swordshield is much bulkier than a 1D sword, which means it will be harder to handle in an agile way. All of this means that 2D swordshields are worthless in a real fight, and the only likely place you'll see 4D parrying is at the circus where 2D swordshields are used for comic effect.
So basically, there is no 4D swordfighting in any practical sense; there's only armed combat where combatants wield both a sword and a shield (with 3D surface area).
Having said all that, though, the real situation is a bit more complicated. For one thing, it's awfully hard to hit anything with a 1D sword: the 3 degrees of freedom (assuming you stand on the ground and don't jump) means that it's very easy to dodge incoming blows. Given this fact, it would seem that 4D fighters would be chosen for their dodging skills, and that dodging would play a much more important role than in 3D. This also lends some credence to the 2D swordshield, since with those things, it's easier to actually hit something even if they are more cumbersome to handle. Also, you won't be able to cut things effectively with a 1D sword: even if you hit your target, it would only amount to a piercing blow rather than a severing blow. You don't stand a chance of cutting off limbs with a 1D sword; you need a 2D swordshield for that. Still, if you strike in the right spot, you can probably hit some vital organs and disable your opponent, perhaps for just long enough that you can move in with the cumbersome 2D swordshield to sever some limbs without the risk of getting hit yourself.