How to add a div around the default gallery output

Well, since you don’t want to edit core files (which is absolutely fine, and unnecessary) and also don’t want to do it by means of PHP (meaning functions.php, for instance), here’s a jQuery approach:

$('div[id^="galleryid-"]').wrap('<div id="SOME_ID" class="SOME_CLASS" />');

BTW, you know there already is a container div that you can hijack for CSS purposes, right?