Maybe try adding the path to the newsletter.php page itself with the other configuration options. That should overwrite the setting in the config.js file:
$CKEditor_config["filebrowserBrowseUrl"] = "/webassist/kfm/index.php?uicolor=eee&theme=webassist_v2&showsidebar=true&startup_folder=cms_files";
That way you can add ../ in front to make sure it goes to the correct location. Another option might be to just copy the webassist/kfm/ folder and paste it into the admin/webassist/ folder so that it can be found there as well.