The SafeZone really isn't intended for general browsing, but for the likes of on-line banking or visiting sites which are security or confidentiality related. The idea of the SafeZone is that it is isolated from your regular desktop and uses a customised browser (safezone browser), based on chromium within the safezone.
You can run your regular browser in the Sandbox (of course you have to have avast Pro or AIS) and that should allow for your normal use of your regular browser, but isolated in a sandbox. Or run your normal browser (which is ?), but beef it up if your only concern is cookies ?
Cookies really aren't an issue, certainly not a security issue but a minor privacy issue possibly. - See
http://en.wikipedia.org/wiki/HTTP_cookie.
- The main issue with cookies are third party cookies, those that aren't for a site that you are viewing, they can track your browser usage and activity for that site other site (shopping, etc.). Depending on your browser (?) you should be able to block third party cookies, you can also set your browser to clear your cookies when you close it.
Since I use Firefox 6.x, I also have the cookie monster add-on and by default that only allows session cookies; they are only valid for the time you have your browser is running. The cookie monster add-on also allows you to accept cookies (normal time limited ones) for a site, like forum.avast.com as cookies are used so you don't have to logon all the time, etc.
All of the above helps remove the need for you to manually manage cookies.