I don't have HOTD: Overkill or the Perfect Shot but I don't see why it would have issues with the game, seeing as it is really just a plastic case.
With the Perfect Shot slightly raising the height of your Wiimote perhaps it could be something to do with the position of your sensor bar though. Maybe try moving it and see if it makes any difference.
How long of a game is HOTD: Overkill? I've already spent my February gaming money on Tenchu and March's is going on Madworld but if Overkill is decent in length then I might pick it up later on.