Jill,
Are you hosting your feature service on ArcGIS Online or on your own ArcGIS Server?
If ArcGIS Online, how did you publish it to online? What was the source of the data, e.g., shapefiles?
Basically, if you're publishing from ArcGIS Desktop, and your data has domains defined, these will come through when editing attributes. If you published a shapefile, there are no domains, so we will only populate a dropdown when editing for the field you symbolized. Thus, it would not be possible to display a single symbol and have the editing dropdown.
If your feature service is hosted, go to the item details page of the service, and click Edit. There is an option that allows you to control what kinds of edits can be made. One of the choices is that only attributes can be edited.
Thanks,
Mike