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Hi,
The logic behind ArcGIS Viewer for Silverlight Add-in and ArcGIS for Desktop Add-in is quite different. There is no way you could use the add-in from Desktop in Silverlight Viewer directly. Neither can you "recompile" the add-in to match Silverlight standards.
You will need to write an Silverlight Viewer add-in from scratch (or by using samples). Naturally you could take the idea behind Desktop add-in (written in C# or VB, for instance) and then use it as a reference when writing Silvelight add-in using ArcGIS API for Silverlight.