The risk here is more insidious than the UN, itself, enforcing its will. As you say, the UN itself has little real power.
The risk presented by a treaty like this is multi-fold.
1) IF the member nations ever get on the same side of the fence and vote to adopt a treaty, and our President signs it, it is very close to being a law of our land. The Senate has to ratify it, of course, but we just never know which way that body will swing, year to year, and depending on the specific language of the treaty. If nothing else, the fact that a popular President comes out in favor of the consensus of "the whole world community" and signs a treaty means that we and our allies have to spend a lot of political capital (and REAL capital) to fight it. If we can't overcome that political will/momentum, the treaty becomes the law of our land and our law enforcement agencies enforce it as such!
2) Even if we don't ratify it, if OTHER nations ratify such a treaty, it may directly affect gun sales and support in the US. If nations like Italy, Brazil, Russia, the Czech Republic, Croatia, Belgium, Turkey, Spain, Romania (and many other former eastern-bloc states with stockpiles of surplus weapons) etc. decide that personal small arms need to be restricted, registered, or eliminated, those important sources for weapons WE enjoy may dry up, disappear, or present significant regulatory hurdles to the American consumer. (I'm not sure whether this is at all likely but someone else postulated it so: I don't want to be filling out an "End User" certificate for my new CZ to go on file with the UN even LESS than I want to fill out a registration of that weapon to our own BATFE.)
We do need to be vigilant about this. But we need to be scrupulously clear, factual, and honest about it as well. That means we should avoid "Chicken Little" panicky hyperbole because that distorts and obscures the real threats, and we should not accept blanket statements like "The NRA stopped...." preferring instead to understand exactly where we stand and what tactics can and will work.