I’m exactly looking for the same thing, but also considering a way to edit what the widget prints (basically to hide some things displayed by the widget that I don’t want to show, but they’re not between tags to hide them using CSS).
Oh boy! I’ve just found the T2 Template option: It’s absolutely brilliant!!! You can edit or create your custom widget template for any widget and then using it on your theme through <?php echo do_shortcode('[shortcode]'); ?>
or directly with the functions from the documentation (though, I prefer calling it on a widget area)
Really, it’s one of the best options I’ve seen on any plugin. This is so perfect. I didn’t even have to change my CSS.