Lets start with the fact that you cannot legally redistribute a single .Net DLL with your application.
Next lets make sure you understand the purpose of the Client Profile; and it is to provide a smaller footprint for distribution and/or a faster deployment experience for you users. It does this by providing a streamlined subset of Windows Presentation Foundation (WPF), Windows Forms, Windows Communication Foundation (WCF), and ClickOnce features.
Based on this you need to decided if the Client Profile meets your goals for your application.
If it does, you will need
to refactor your project to not be
dependent on any libraries that are
not part of that profile.
If it does not then you really shouldn't
be using the Client Profile.
As I see it you only have those two options.