The real question is whether meat has be completely passing through the ring hole.
If that's the case, sticking it in his butt would probably work too since a lot of your intestines are innards are squeezed together enough to essentially be flat. If it's being pushed along on it's side with peristalsis and any of of your bowels touches through the ring hole... you turn invisible for a minute.
Just imagine how strange it'd be seeing a halfing pop in and out of existence running at you with a blue sword that can tell him that you're nearby...