But....Zero weight would still mean zero weight which means how would they come crashing down to begin with and also how would they survive plummeting from the sky at high speed if they did? The skyships can fly because they vary their weight using a very very careful and precise system of ballasts to keep themselves level and prevent floating off into space and also to allow them to land if I've read things right. How would you make their weight variable and even if they did crash down, with no weight behind it at all wouldn't the impact be insignificant regardless of the size of your sword? The mass would be significant but it doesn't weigh anything which is how you seem to be saying you'll lift it in the first place so the strike wouldn't fall very heavily.I may not be right about this either but it seems confusing.

Also regardless of whether mass influences falling speed, air resistance certainly would and a massive sword would have a lot of air resistance that might affect your momentum

Furthermore a weightless sword probably wouldn't cut very well since only the human's momentum would be driving the force behind any given swing but that's not even relevant compared to the other problems.

and I'm really sorry, I don't mean to be one of those irritating nitpicky people, I'm just confused as to how it would work.