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Sure, happy to share the source, though you're welcome to use a disassembler or reflection tool as well -- easiest thing would to fill out the Source Code Request and we'll email it on over.
If you only ever had a single, well-known database to work with, then hard-coding the connection string isn't too bad of an idea. You can always just update the code and redeploy the extension if it ever changes. But since you have multiple databases... I'm not sure if it's the best approach.
Otherwise, consider that any property on your class that you mark with the Persistent will be displayed as a textbox and it will be available at runtime. So, two ideas come to mind:
You could have a ConnectionSTring property, and just use that; that would be quite easy
You could have DatabaseConnectionName property, and have that reference a database connection within your application; these are used to deploy database changes
The DatabaseConnectionName will be a little trickier, as you'll have to retrieve it from the database, then deserialize it, then look at the object's connection string property. All of the Database ACtions do this, so you can look at their source code.
You'd only want to do this if you're already using database connections.