This simple module and xphp snippet produce a link to edit the profile being viewed on any profiles details page regardless of login status.

profile.php

...

            <xphp content="true">
              <if var="profiles_edit_link"/>
              <content>
                <div class="profiles_edit_link">
                  <xphp var="profiles_edit_link" inner="true"/>
                </div>
              </content>
            </xphp>

...

public.application.profiles_edit_link.php

<?php

$_LW->REGISTERED_APPS['profiles_edit_link']=array(
	'title'=>'Profiles Edit Link',
	'handlers'=>array('onWidgetFormat')
);

class LiveWhaleApplicationProfilesEditLink {

  public function onWidgetFormat($type, $handler, $variables) { // alters widget variables before widgets are produced
    global $_LW;
    if ($type === 'profiles' && $handler === 'details') {
      if (empty($GLOBALS['profiles_edit_link'])) {
        $GLOBALS['profiles_edit_link'] = '<a href="/livewhale/?profiles_edit&amp;id='.((int)$variables['id']).'" title="Edit '.$_LW->setFormatClean($variables['firstname']).'\'s Profile">Edit This Profile</a>';
      }
    }
    return $variables; // and return the variables
  }

}

?>