I think you're asking "after my C# server code sends a redirect to the client browser, telling it to go somewhere else, I want the browser to NOT put my site URL into the Referer header when it goes to that somewhere else"
You can't, if it's direct, unless you're redirecting from a secure page (yours) to an insecure page (theirs)
You'll probably have to create an interim page that you redirect to, that has some client side scripting that performs the actual transition (like those "thanks for searching your flight with expedia, please wait while we transfer you to the airline to complete your booking" type pages) because then you can take control of what their browser sends; if you straight refer them, you can't