Is there a way to add a variable to an "a href" to show what blog to point to?

I am working on a multisite using subfolders (not subdirectories) for each site. I have a requirement to make all necessary editing on the front end so the users won't have to go into the admin menus for anything. I am using a template which is used when people create new sites. I am trying to get the theme customize page (wp-admin/customize.php) to show as a button on the front end and am trying to do this using "a href=". My issue is the url on the template page is "http://diplomakids.pleth.net/newchildtest/wp-admin/customize.php?url=http%3A%2F%2Fdiplomakids.pleth.net%2Fnewchildtest%2F" where the "newchildtest" is the name of the template file. I am trying to make this dynamic so that part will be whatever the name of the site is (i.e. if the site name is "testchild" then the url should show "http://diplomakids.pleth.net/newchildtest/wp-admin/customize.php?url=http%3A%2F%2Fdiplomakids.pleth.net%2Ftestchild%2F"). I figure there must be a way to use a variable to do this but not sure how to do it. Any thoughts on how to do this or if there is a better way of doing it rather than "a href"? I tried menus but couldn't find a way to make it dynamic to the specific site so it wouldn't change the template file. Any help on this would be greatly appreciated. Thanks!