If I'm telling Billy to put on his shoe, and if I were being absolutely correct, I would say, "Please put on this shoe, Billy". If I said, "Please put this shoe on, Billy", then it would sound as though I were asking someone else to fit the shoe onto Billy's foot. Likewise, if I just said, "Put this shoe on", the other person might think, "Put it on ... what? My foot? The table?"
In reality, if I were saying it in my uneducated, Leicester way, then I would indeed end up saying, "Please put this shoe on".