You have no need to be worried; unless the jw.org site installs an ActiveX control or something like that on your computer, they can't read your cookies from other sites.
http://www.perlservices.net/en/faq/cookies.shtml#nine
When a cookie is written to your computer by jw.org, only jw.org can read it--yahoo.com can't read it, google.com can't read it, and neither can any other site. Vice versa is also true. Your browser enforces that security--it will only return cookie data to the site that originally wrote the data. And, without an add-in ActiveX or Java control that you "allow" to be installed, a site can't tell what your browsing history is, either.
If you're really paranoid, use the Chrome (http://chrome.google.com) browser's Incognito window, or the Tor Firefox add-in, or run a program like CleanUp that deletes all previous cookies and browsing history from your system before you log into the jw.org site.
For the truly paranoid, install a Virtual PC image on your computer, or setup a totally separate physical computer, and use it for NOTHING other than logging into jw.org.