Maybe the simplest solution would be to configure WCF client programatically within CLR DLL library?
var binding = new System.ServiceModel.BasicHttpBinding();
binding.SendTimeout = TimeSpan.FromMinutes( 1 );
binding.OpenTimeout = TimeSpan.FromMinutes( 1 );
binding.CloseTimeout = TimeSpan.FromMinutes( 1 );
binding.ReceiveTimeout = TimeSpan.FromMinutes( 10 );
using (var client = new SomeServiceSoapClient(binding, new System.ServiceModel.EndpointAddress("http://site.example/SomeService.asmx")))
{
// client.DoWork(...)
}
and pass configuration data (URL) as argument to the SQL CLR function? In this way you are independent from the app.config location problems.