This is a good question and one that doesn't have a clear answer.
One would assume that it would happen using modern weaponry (whatever that happens to be at the time), and there are some narrations suggesting the Dajjal might have some sort of modern machinery, and some of the signs of end times seem (God forbid) similar to the results of modern warfare. From this angle, the word "swords" in narrations could be taken as a figure of speech to represent weaponry.
However, it is also entirely possible that, at that time, something will have happened to make modern technology unworkable. (Some people have suggested a magnetic pole shift; one could also consider a massive solar flare, or really anything that would result in the destruction of the means of production or use of such items such as an environmental crisis.) This would also be concordant with the general description of chaos preceding the arrival of the Mahdi (A).
So, basically, there is no clear evidence either way; it is one of those things which we will have to wait and see. Of course the important thing is to be on the side of the Imam (A), regardless of what kind of technology is available.