What is incumbent upon a person who swore an oath regarding something under another's possession, that he would use it, but was not given permission to use it, and he said aloud: "By Allah, I will use it tonight," then secretly followed it with "if Allah wills"?

Whoever says "insha'Allah" (God willing) intending to make an exception, is not guilty of breaking an oath, whether he says it aloud or to himself. And the one to whom an oath is made should fulfill the oath of the one who swore it, unless it causes him embarrassment, due to the hadith of Al-Bara' that the Messenger of Allah, peace be upon him, commanded the fulfillment of the oath of one who swears.