“We ourselves have sworn to them by Yahweh.” The leaders did not want to take the name of Yahweh in vain and make a false oath (cp. Exod. 20:7; Lev. 19:12; Deut. 6:13; 10:20).
“touch.” Idiomatic for “harm.” The Israelites were supposed to kill the Canaanites (cp. Josh. 9:26), but they cannot harm the Gibeonites. “Touch” is used for harm (including rape) in Ruth 2:9. The leaders took the oath they had made very seriously, so seriously that it superseded the command of Yahweh in the Torah about what to do with the people who lived in the land. This is a good example of one law in the Torah being greater than another, and there are no clear directions from God as to what to do when that occurs (generally because the situation occurs, as it did here, with human error). The leaders must have considered that scriptures such as Leviticus 19:12, and Deuteronomy 6:13 and 10:20 superseded God’s command to destroy the Canaanites. It would be interesting to know if Rahab’s family being among them had any influence on that decision—but there is no way to know that.