Removing extra 10px of width for captions in TinyMCE editor

I’m successfully using the below to remove the 10px of width added to captions by media.php. However, I still get the 10px of added width in the editor. What can I do to remove the 10px (or even the entire width value if that’s easier) within the editor?

add_shortcode('wp_caption', 'fix_img_caption_shortcode');
add_shortcode('caption', 'fix_img_caption_shortcode');

/**
 * The Caption shortcode.
 *
 * Allows a plugin to replace the content that would otherwise be returned. The
 * filter is 'img_caption_shortcode' and passes an empty string, the attr
 * parameter and the content parameter values.
 *
 * The supported attributes for the shortcode are 'id', 'align', 'width', and
 * 'caption'.
 *
 * @since 2.6.0
 *
 * @param array $attr Attributes attributed to the shortcode.
 * @param string $content Optional. Shortcode content.
 * @return string
 */
function fix_img_caption_shortcode($attr, $content = null) {
	// New-style shortcode with the caption inside the shortcode with the link and image tags.
	if ( ! isset( $attr['caption'] ) ) {
		if ( preg_match( '#((?:<a [^>]+>\s*)?<img [^>]+>(?:\s*</a>)?)(.*)#is', $content, $matches ) ) {
			$content = $matches[1];
			$attr['caption'] = trim( $matches[2] );
		}
	}

	// Allow plugins/themes to override the default caption template.
	$output = apply_filters('fix_img_caption_shortcode', '', $attr, $content);
	if ( $output != '' )
		return $output;

	extract(shortcode_atts(array(
		'id'	=> '',
		'align'	=> 'alignnone',
		'width'	=> '',
		'caption' => ''
	), $attr));

	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: ' . (0 + (int) $width) . 'px">'
	. do_shortcode( $content ) . '<p class="wp-caption-text">' . $caption . '</p></div>';
}