I think you're asking the wrong question here. Instead of asking whether this is "citation stuffing", I would suggest you simply ask yourself whether this makes the paper better or worse (or no different) for your reader. That is always the ultimate question that should inform all other choices.
Given that you are only proposing to add a single sentence to the paper, citing some purportedly related works, it is not onerous to read that additional sentence. If the papers are indeed related enough to be of interest to some readers, then it is probably not going to make your paper any worse to mention them. Bear in mind that when you read an academic paper about a particular problem, you are often interested in related problems, even if they are variations that are different to the immediate problem. On the other hand, if the papers you propose to cite are not really related to the topic at hand, or are too far removed to be of interest, it will be annoying if you lead the reader to them on the basis of a false promise.
As to the fact that you have only "skim-read" the papers you propose to cite, that is not necessarily disqualifying, but you need to be careful. If you're going to say that these works are "addressing this problem, as well as its variations", then you have to make sure that you read enough to be absolutely sure that this claim is true. It is also important to have read enough of them to be satisfied that these are good papers ---i.e., you want to direct your reader to papers that are valuable for them to read. You don't necessarily need to read an entire paper to know that it relates to a variation of the problem you are working on, but you have to make sure you read enough that you are not just guessing or taking someone else's word for it.