Add custom Attachment Display Setting for images

I’ve been doing a lot of research and I’ve yet to work this out. Can you add in a custom option in the Attachment Display Settings (part of Insert Media dialog in post editor)?

What I’m after is the ability to add an anchor with a class around all images in posts.

This will add a field in the attachment edit screen for applying a class to the img tag.

function IMGattachment_fields($form_fields, $post) {
    $form_fields["imageClass"]["label"] = __("Image Class");
    $form_fields["imageClass"]["value"] = get_post_meta($post->ID, "_imageClass", true);
    return $form_fields;
}
add_filter("attachment_fields_to_edit", "IMGattachment_fields", null, 2);
function my_image_attachment_fields_save($post, $attachment) {
    if ( isset($attachment['imageClass']) )
    update_post_meta($post['ID'], '_imageClass', $attachment['imageClass']);
    return $post;
}
add_filter("attachment_fields_to_save", "my_image_attachment_fields_save", null, 2);