I created the ArcGIS widget available from the Marketplace. If you are using that one, still based on Dojo, you need to alter the code to being able to handle shape files.
Some Esri example code can be found here:
As for the client delivering various different formats, I would try to make sure only one format is used and making sure all other formats are parsed to that one format agreed upon. Else the process as well as widget will become unnecessarily complex