I use unrefined oils (cold and expeller pressed). I just do this because I don't want anything processed. I really don't think there is anything to fret about. Both will work fine. For sesame oil, you just don't want toasted, because that does remove the good properties of the sesame seed.
The sunflower oil I get is organic, and expeller pressed.
I'd just continue on and see how it goes. You're doing fine.
Next time you are in a health food store (if that's not where you've been already) check out their oils.