Hi,
Export to DXF and Shp is currently not support by ArcGIS Runtime.
Good options for sharing data are ArcGIS Feature Collections (which can be shared directly as JSON or via ArcGIS Portal Items) and KML.
Did you mean you are using ArcGIS Runtime SDK for .NET (Esri.ArcGISRuntime.UWP) instead of ArcGIS Runtime SDK for Windows Store Apps?
Thanks
Mike