Numbers 20:19

It is just nothing. Nothing at all will harm you.

And Israel said to him, We would go by the king's highway; if we drink thy waters, I and my cattle, I will give thee the price of their value. I will only pass through, without doing wrong.

AND THE CHILDREN OF ISRAEL SAID UNTO HIM: ‘WE WILL GO UP BY THE HIGHWAY.’ At first they had said that they would come into the cities, but would take care not to enter fields and vineyards as armies [consisting of] many people are wont to do, in order to plunder the threshing-floors and to invade the vineyards. Instead, they [promised] to go along the king’s highway, which is a public thoroughfare, (the king’s highway) is explained as a definite official highway which followed the eastern bank of the Jordan. Ramban’s interpretation is thus unlike Ibn Ezra’s who explains it to mean the way which the king of Edom will specify for their passage. not a private road. Furthermore they said [at first] that they would not drink any of the water which they [the Edomites] have in their wells for their own needs. Afterwards the Israelites sent them a message [saying] that they would not [even] approach the cities at all, but they would go by the highway which leads up to the land of Canaan, which is a paved road traversed by all people, and if they or their animals drink [even] of the waters of the rivers on the way, whilst passing through the rivers, they would pay them for the benefit they derived from them. Therefore Moses said [here in Verse 19] there is no hurt, meaning that in [passing through their land] there would be no damage of any sort. Other scholars explain [that they meant to say] we shall not drink of the water of the wells unless we pay for it. But this is not correct, for [if so] why would he [Moses] propose to them again that which he [the king of Edom] had already refused at the beginning? [as explained in Verses 17-18]. The Midrashic interpretation 12. According to this explanation Moses was offering to buy from the Edomites their water, although the Israelites could have drunk freely from Miriam’s Well. is: “We shall not drink of the waters of [our own] well, but instead we will buy from you,” as Rashi wrote.
Israel said to Edom, until we have passed thy border and they did not say to him [“and we will reach] the Land which the Eternal our G-d giveth us” [as they told Sihon king of Heshbon], in order that Edom should not be jealous of them [taking possession] of the Land, and [should not] claim that it would be theirs [the Edomites’], had not [Jacob] taken [Esau’s] birthright and blessing from him with guile. But to Sihon they did mention, until I shall pass over the Jordan into the Land which the Eternal our G-d giveth us, as Moses stated in the Book of Deuteronomy.

במסלה נעלה, Moses argued that if they were to cross through towns and come into contact with the inhabitants there might be concern about possible friction, but it was their intention to cross the land in areas that were totally uninhabited so that there could not be a question of possible friction and war.

רק אין דבר ברגלי, we have not even with us anything that could become the focus of a quarrel.

אעבורה, seeing that your only concern is possible friction and you do not object basically to our traversing your territory we will proceed to cross it seeing that you have nothing to fear.