Alfresco 4.2.c provide functionality called "Quick Share" sharing a link publicly but it generates short URL. Can we have full URL so any customization on shared page can be done?
There is a URL rewrite filter (defined in the urlrewrite.xml file that you'll see in the WEB-INF directory) that maps anything with /s/ in to /page/quickshare?id= where the id is set to the value after /s/ in the URL. The id needs to map to a valid shared node. If you want to customize the quickshare page then you'll need to customize that page.