I have a web service that I invoke from script but that does not need any information stored in cookies. Anytime I make a request to the service, the cookie is sent along with i
No, the cookie will always be sent.
You could how your cookies are sent to the browser, and use the http flag on them, which means they won't be sent via javascript.
http
Or (which lots of sites use), create a new subdomain which you never sent any cookies on.