Wordpress - replace wp_get_attachment_image with my own function

There is a filter, wp_get_attachment_image_attributes, for the image attributes-- a well designed one too.

function alter_att_attributes_wpse_102079($attr) {
  $attr['data-src'] = $attr['src'];
  return $attr;
}
add_filter( 'wp_get_attachment_image_attributes', 'alter_att_attributes_wpse_102079');

That will add the data-src attribute. That looks like what you need. You could add more attributes, or alter the existing onese, if you need.