I think the OP plans to pick up the friend and the car at the same time, not pick up the rental car late the previous evening.

If the OP doesn't want to take his own luggage on the hotel shuttle to the airport and then the rental car shuttle, he/she could ask the friend to come to his hotel in the hotel's shuttle. The rental car could be picked up and driven to the hotel whenever it's convenient, especially if the hotel has free parking for overnight guests. If OP doesn't check out first, friend could freshen up in the room before leaving for Sedona.