You can make a very small bias tape or binding from strips of necktie (already cut on the bias).  Cut 5/8" wide strips from a thin silk tie and make 1/4" tape using a bias tape maker.  (Pressing with a steam iron will help set the creases.)  Then fold the tape in half, matching the folded edges and press again.  You should have bias tape that is approximately 1/8" wide that you can now hand-applique and bend as you wish.