Wow this is just incredible, if you have not ordered yet, heck even if you have you can change it, just get the factory tow package.
At $395.00 it is a bargain, you get "Class II Trailer Tow Package: Class II receiver hitch, engine oil cooler, larger radiator, upgraded battery and cooling fans, wiring harness and 4-pin connector", and it does not hang down below the rear valance, like aftermarket ones do.
Even if you never tow, the oil cooler is still working for you, not to mention resale appeal.
You are going to spend around $33,000, don't cheap out over a few hundred.