You can invoke a CLickOnce application by linking to the deployment manifest (the .application file on the webserver) (assuming it's deployed via the web), AND you can pass query parameters to it if it is an online-only application. You also have to have the option in the publish options set to allow URL parameters to be passed to the application.
How to retrieve query string information :
http://msdn.microsoft.com/en-us/library/ms172242(VS.80).aspx
I think this is your best bet. From the desktop, you can run the application even if it's offline, and pass parameters to it, but from a website, I think this will work best for you.