Im assuming its as easy just to use "absolute" URLs and use www.........
absolute URLS would be the full URL of any given page:
such as index.php
a relative path to the above (in coding on your website) would be: index.php (or ../index/php or ../../index.php (depending the folder depth where you are)
so any secured pages would need to be admin.php
if im also right i beleive in theory even if you dont have a secured certificate if you still use HTTPS:// in any page reference it would still have some kind of level of secruity on shared hostings.