I don't know if expanding the palate widens your nostrils. I think it's more that the bridge of your nose may expand and your nose as a whole gain better support. Some people here have claimed to have seen their noses straighten out a bit, as a result. If the maxilla expands, then the entire midface should theoretically widen, so even if the process widens your nostrils, it also widens other features, meaning that the changes occur more-or-less proportionally, and possibly won't have negative aesthetic effects. I wouldn't really worry about such things; I'm allowing my face to be affected by a good oral posture in whatever way nature sees fit. I trust that in addition to health benefits, the end result will positively impact my aesthetics, even if certain features are affected differently than others.

Yes, a real skeletal expansion (that splits the midpalatal suture) widens the base of the nose. But that widening is barely noticeable, and it could always be addressed afterwards with an alar base reduction.