In the Netflix show Tokyo trial the judges that were in charge of the war crimes tribunal had it put to them by the legal defence team that war in of itself was not an illegal act despite the Pact of Paris condemnation. In the show they further put forward that if killing in war (or as it was categorised then Crimes Against Peace) were illegal then America and all people involved with planning and execution of the nuclear attack on Japan held criminal culpability as well. Was this a concern for America at the time? And were there any legal proceedings to ask and answer if America should be held to account for that attack?
There is no evidence that I have seen that legal issues were ever part of the consideration with regard to the use of nuclear weapons. The US did worry about world opinion, especially after the massive reports of casualties, and worries about radiation poisoning, seemed to sour many people on the use of the weapons. But this was not a legal concern so much as a diplomatic one. There were no legal proceedings that I know of that tried to censure US conduct during war with regard to bombing. It would be difficult to make a strong legal argument given that the bombing of civilians was practiced by all sides during the war, and given that the war tribunals were exclusively run by the victors.