Feature services, by design, provide access to the geometry of the underlying features. Is your feature service a hosted feature service or running on ArcGIS Server? If it's hosted on ArcGIS Online, you can publish a hosted tiled map service of it. Go to the feature service item and you will see a publish button. Tiled map services consist of a set of tiled images that are used to display the data. No geometry is available as the display is just a static image.
If you're running on arcgis server, you can create a map service and, I believe, disable the "data" capability. Or also create a tiled service.
THanks,
Mike