This will remove the draggable functionality from each widget:
You have find a good way to inject this into your code, either through
wp_enqueue_script() or echo it inline on the Widget page.
To target a specific Widget you would have to do something along these lines:
if (jQuery(this).find('h4').text() == 'Archives')
Or select your way around to find the widget by
If you browse around the source you'll soon find out how these are internally formed by WordPress. The rest is up to jQuery, selectors, maybe regular expressions (though I don't recommend them in this case).