I have an existing dimension feature class that I would like to change a reference scale of.
Is that possible or do I have to always create a new one, with desired reference scale, and then import styles from existing one?
At one time there was an ArcGIS Idea for ArcMap that seemed to cover the functionality that you seek but that link can no longer be reached.
Now there is an ArcGIS Idea for ArcGIS Pro to do it instead.
See allow dimension feature class property changes AFTER the feature class has been created.