A time traveler is back in time around the time that the US is considering using Nukes, the time period is already modified such that there is no longer a guarantee that brinkmanship won't lead to nuclear war. The above question's consensus seems to be that the nukes will still be used in much the same way they were now. It also seems many stressed that the nukes of Japan were partially to show off their power to discourage Russia, not just to defeat Japan.
So assume that nukes are going to be used in WW2 in much the same way they were in our timeline. However, the time-traveler warns the US of the Nuclear brinkmanship, risk of nuclear winter, and general terror that this all lead etc. He also points out that Russia will get nukes soon since anyone can research it, and spies are heavily involved in stealing US nuclear secrets; the time traveler lack of knowledge and changes in the timeline mean he can't tell them what spies to expect or how to avoid a leak.
The time traveler encourages a policy to the high ups to try to avoid escalation by setting policies on proliferation when they are the only ones with nukes. He suggests the following.
First, as much as possible the US publicly acts upset and horrified by the nukes as they can politically both before and after their use. Play up the "were only using nukes because we think it will save more Japanese lives in the long run, but were still very sorry to use them" whoever they can. After using the nukes pretend the US didn't realize how powerful they would be and are thus even more upset about using them; they start talking of their 'realization' of the threat of nuclear winter if nukes become weapons of war.
Then, immediately after Japan surrenders they propose an anti nuclear proliferation accord; or alternatively perhaps they suggest making the new United Nations roles include preventing proliferation and members of the UN must agree to some anti-proliferation policies and back the UN in enforcing those policies.
In any case the basic treaty sets rules such as limiting the maximum number of nukes to a small number, specifying situations where nukes may not be used in warfare, indicating that countries agree to enacting strong sanctions on violators of the treaty, from trade to declaration of war etc.
The general idea behind this is that everyone is likely to be behind signing something like this while the US still is the only one with Nukes, because they are only restricting abilities they don't yet have and limiting how much the US can exploit their power. The rules are reasonable enough to make most people want such non-proliferation rules to exist in any case, and thus want to sign such a treaty, particularly with fears of the nuclear winter scenario the US describes. Thus it should be easy to get people to sign such a pact as long as the US holds the only nukes.
However, the pact is written in such a way that it does not directly outlaw any use of a nuke, only on mass proliferation and certain egregious uses. Thus the US, as the only nuclear power, is still able to use their nukes to intermediate countries like Russia since they are legally allowed to use them on the small scales they would likely want them for at that time. The pact only becomes relevant once you have two nuclear powers tempted to escalate leading to buildup of weapons. Thus the US is not sacrificing much of it's current bargaining power by backing the treaty, and may be able to use it's nukes to encourage treaty policies that are good for them, such as sanctions on people trying to develop nuclear capabilities to maintain their nuclear superiority for some time.
Given this general advise for moving forward would the US be willing to attempt it, and would it work? That is to say, would the US be too loath to give up their bargaining chip even if it meant avoiding later danger and/or the politicians afraid of the public opinion of voters if they try? If it was enacted, would it even work or would both sides pretend to abide by the treaty while still escalating?