(The rate wouldn't be higher for a particular night if you are staying 1 night instead of 2.)
They don't let you just drop a day or days at the beginning or end of a reservation any longer (changed years ago). You have to be able to rebook, basically. Or convince a manager on the phone to grant some pixie dust. I.e., some resorts will show no available rooms for 1 night ressie, but will show rooms available for several nights (covering the 1 night that showed as not available). Hope that makes sense.
Basically you might get lucky and can make that change online, if not call and request a manager to help you out. Or book two reservations and cancel one once you know what you need (I don't like that practice but understand it).