As you say, in web.config, you can specify that the contents of the appSettings section come from a separate file. Use this to import the shared settings. Like this:
<appSettings file="..\..\config\appSettings.config" />
The file path you specify is relative to the location of web.config. As shown above, you can simply use ..\ notation to reference a path outside of the web root. That means you can maintain the shared config file wherever is convenient.
See http://msdn.microsoft.com/en-us/library/aa903313(v=vs.71).aspx for further details.