This is a matter for individual characters, which we each may play many different instances of.
If your main focus is playing a chaotic character, though, generally swearing an oath to someone isn't going to get in your way as a concern; chaotic characters generally act as they feel is right in the moment - what is 'right' for them will vary along the other half of the spectrum, but they generally won't feel constrained by what is 'expected' of them, legally or socially, if their feeling for what is right in this particular moment runs against those things.
In this sort of situation, generally speaking, a chaotic character who feels that they need to acquire the poison from Nettie, and has that as their immediate personal goal, or who just wants to resolve the situation peacefully, won't get too hung up about swearing to her, if that's the most straightforward way of doing that and it doesn't run against any of their other personal inclinations. If you're playing a character who feels strongly enough that an oath sworn should be kept, and will also not swear an oath that they intend to break, even though refusing this will negate their actual goals, in order to keep to that, then you are really playing a more lawful character than anything else; lawful doesn't necessarily mean following social legal codes, it just means putting codes of conduct or principle ahead of your personal views on right action if the two conflict.
I generally play chaotic characters most commonly, and most of them will make the promise to nettie to put her at ease, even if they have no intention of actually doing what she asks; if they feel she's misguided in what she's trying to do, but can't convince her of that (due to lack of conversation options), then just putting her at ease and getting her to let them move on unhindered is the next best thing, and it doesn't really matter if that involves making a promise they've got no intention of keeping to - especially one about ending their own life.
