It doesn't look either shortcode—on its own or in combination—is able to output the user nicename for the current user.
You can output the nicename with the wpv-user shortcode, but cannot specify the current user.
You can specify a specific user via the id attribute, so I suggest you register a simple custom shortcode that returns the ID of the current user, and use that to provide the value for the id attribute of the wpv-user shortcode.
So the shortcode would be like this:
add_shortcode('current-userid', function () {
$uid = get_current_user_id();
return $uid;
});
Then register this shortcode so that it can be used in Views shortcode arguments, at Toolset > Settings > Front-end Content > Third-party shortcode arguments.