WordPress: Stripping Images of <p> tag and adding <div> IF image has no caption

I’ve seen some variations of this question around, but I’ve as of yet been unable to tweak them into what I’m looking for.

In a WordPress post, if an image is uploaded with a caption the image will be output wrapped in a div (with class wp-caption). Perfect.
However, if there is no caption the image is wrapped in a paragraph tag. I’d like to replace this with a div.
So if an image is uploaded without a caption, it is wrapped in a div as well — something like class=”wp-nocaption”.

My first try was to modify the media.php file. I changed this section:

if ( 1 > (int) $width || empty($caption) )
  return $content;
if ( $id ) $id = 'id="' . esc_attr($id) . '" ';
  return '<div ' . $id . 'class="wp-caption ' . esc_attr($align) 
  . '" style="width: ' . (10 + (int) $width) . 'px">'
  . do_shortcode( $content ) . '<p class="wp-caption-text">' . $caption . '</p></div>';

to this:

if ( 1 > (int) $width || empty($caption) )
  return '<div ' . $id . 'class="wp-nocaption ' . esc_attr($align) 
  . '" style="width: ' . ($width) . 'px">'
  . do_shortcode( $content ) . '</div>';

if ( $id ) $id = 'id="' . esc_attr($id) . '" ';
  return '<div ' . $id . 'class="wp-caption ' . esc_attr($align) 
  . '" style="width: ' . ($width) . 'px">'
  . do_shortcode( $content ) . '<p class="wp-caption-text">' . $caption . '</p></div>';

Which I hoped would do the same thing for a non-captioned image as a captioned one, except the div would have a different class.

But that didn’t work. Does anyone have any idea why?

I also found some articles suggesting using a preg_replace function.

http://css-tricks.com/snippets/wordpress/remove-paragraph-tags-from-around-images/

https://wordpress.stackexchange.com/questions/7090/stop-wordpress-wrapping-images-in-a-p-tag

I tweaked their functions, attempting to replace paragraph tags that wrap an image wrapped in a link with div tags.

function filter_ptags_on_images($content) { 
  return preg_replace('/<p>s*(<a .*>)?s*(<img .* />)s*(</a>)?s*</p>/iU', 
  '/<div class="wp-nocaption">s*(<a .*>)?s*(<img .* />)s*(</a>)?s*</div>/iU', 
  $content); 
}
add_filter('the_content', 'filter_ptags_on_images');

But this doesn’t work. I’ve been reading a lot but still can’t wrap my head around the php concept of “backreference”. I know the replace section of my function is wrong, but I’m not sure how to fix it.

If you have any suggestions as to what I’m doing wrong on either way would be very much appreciated!

Thank you so much!!