It states that you possess your shadow. No, it doesn't state you lose your attacks, but you become incorporeal so your normal attacks no longer apply, incorporeal creatures can't hit physical ones. Therefore, they give you the shadow's strength damage touch attack. You only get the one. I'm surprised this isn't obvious due to the fact your buffed familiar almost solo'd a dragon.
If your DM wants to allow you to abuse the hell out of a spell that doesn't at all do what you're trying to do, by all means do it, abuse it, and let your familiar destroy combat with 3d6 str damage. But realize it doesn't say your attacks (natural or otherwise) do strength damage, it says you gain the shadow's str damage special ability.