Why did Edom make a point of mentioning 'the sword'?
Rashi: In response to Yisrael's request, 1 he replied that just as Yisrael proudly referred to their inheritance of "ha'Kol Kol Ya'akov", he was now putting into practice his inheritance of "ve'Al Charbecha Tichyeh" with which he was now coming to meet them. 2
Seforno: What the king actually meant was that commoners of Edom are violent, and for a flimsy reason or squabble between the residents and the travellers, they would take up a sword against the travellers.
Seeing as Moshe addressed the king of Edom, why does the Torah say 'va'Yomer Eilav Edom'?
Ramban: Because the people supported the king's refusal to allow Yisrael passage through their land.