Okay I knew that...
My point is, that there was NO REFERENCE, that this permanent was temporary. It has a ONE TIME use, unlike Graveyard (which is used whenever a creature dies) or Dimensional Shield (which is constantly in use throughout the 3 turns). If you want to say Sundial, for that one it's also included, it's a one time use and then it disappears.
Now your suggestion DOES NOT SAY, that it would disappear. Therefore I assumed it stays there. And it seemed like a ONE TIME USE, so then, Shrink would just occupy permanent space. If you want to make it a one time use card, you have two options. A spell as I suggested (you play the spell, the next card will have half the HP) or a permanent with a LIMIT ON HOW LONG IT STAYS IN THE GAME. So the permanent would not remain there while useless.
Also what would happen if you have 2 of these on the field? Double halving? (obviously you would not want that, so you'd chain them)