Obviously the solution to your problem is just to man up and tell the truth and grow a pair and....
You dug yourself a bit of a hole and now you want to climb out of it with as little to-do as possible. You've realized the mistake and you want to course correct sans "the drama." Kudos.
I'm all for telling the truth without reservation, but I understand that sometimes situations require a few little white lies to keep things running smoothly. No need to shoot yourself in the foot, if things can be handled quietly.
Unfortunately, the only way I see out of this short of some "National Lampoon" type interjection is to just convince your dad to let you handle it...you know, as a sign of your burgeoning manhood...or something.
If you're not close with your dad, then it'll probably be ok. However, and to affirm some of the good advice in this thread, if you are close, then chances are it is going to get out anyway and then it's going to be phenomenally worse.
I hope it works it out for you.