In a sense, I suppose we could argue that the statement above might be a form of both. If we knew more, it might be dramatic irony because we would be aware of what Jig and her partner are talking about. The "simple operation" could be anything, but it becomes clear to us afterward from the conversation between these two characters and the way that the man insists that firstly the operation is very easy and secondly it will repair everything in their relationship that they are talking about an abortion. As it is, this is information that is not immediately apparent to us at first, as we have to make our own inferences about what this "simple operation" refers to.
However, at the same time, there is a sense in which this comment represents situational irony because of the way that, when we understand what it refers to and what is really going on, it adds a much more sinister significance to the otherwise beautiful scene of two lovers drinking together overlooking a spectacular view. There is nothing to suggest initially that there is anything sinister in the scene that Hemmingway presents us with. It is only when we understand that they are debating the death of their child that everything before and after is given a much more chilling significance. There is thus a sudden reversal in what we expect to happen and in what we think is going on in this tale.
The verbal irony in the short story "Hills Like White Elephants" is in what they are discussing. Initially, I had to read it several times before I undeerstood that they were discussing abortion.
Initially the two, man and women, seem just like a nice couple on a trip, but as the story and their banter progresses we see that they are discussing something that seems to be having a more significant impact on the female than the male.
One statement in the story that the girl makes is to the man after he says that he cares about her. She demonstrates her side of the relationship and the seriousness she feels the act of abortion and the decision will be.
"Oh, yes. But I don't care about me. And I'll do it and then I will be fine." (276)
The statement that you listed indicates how irrelevant he sees the idea of an abortion.
"It’s really [a] . . . simple operation, Jig,’ the man said."
One part that I found is when he tells her to come back in the shade so that she will feel better, but in reality he is pressing her to do the very thing that will not make her feel better. He tells her that he will support whatever decision she makes, but there is the underlying pressure for her to terminate her pregnancy.