I have two CCs listed on my Hz account. After the reservation was booked online, I logged in and changed the default (primary) CC to the other one (secondary). When I rented the car, the CC (new primary) charged for the rental was the proper one.

This was a few years ago, before Ultimate Choice was introduced. The CC change was made a couple weeks before the rental. I know contracts are usually printed the day before or day of.

You should be good as long as the CC you want charged is listed as primary in your account.