Hi,
Unfortunately it's not currently possible to edit shapefiles that have been added via dynamic layers. Although it's an implementation detail, the reason is that the FeatureServer endpoint does not support the DynamicLayer capability.
We are working on improved local data support which will also include synchronization with feature services but this functionality will be released as part of the new ArcGIS Runtime SDK for .NET, which includes a WPF API for building desktop applications (i.e. an evolution of the WPF API you're working with now). It will be available in beta shortly.
In the mean time, if you really just want to edit shapefiles then you could try one of the various 3rd party shapefile libraries (it's an open, published format).
Cheers
Mike