To avoid a cycle you really need to transfer all of your old rock to the new tank. The bacteria lives in all of the rock, so if you only transfer one rock then you’ll be transferring maybe 5% of the bacteria, which will not be enough to keep the tank cycled.
The bacteria lives in other places as well, such as on the sand, on the walls of the tank, in any filter media that you have, etc. So even moving all of your rock is only going to be moving a subset of the bacteria. But usually moving all of the rock will transfer enough of the bacteria that you can avoid another cycle.
Initially it sounded like you wanted to reuse all of the rock from your old tank, but now it sounds like that might not be the case? If you do want to go with all new rock, one option would be to put in all of your new rock and get it set up the way you want, then also transfer all of the rock from your old tank to the new tank. Leave it there for several weeks, then over time (maybe once a week) remove one of the old rocks.
As I stated above, the old rocks will bring enough bacteria to keep the tank cycled and over time the bacteria will start to colonize on the new rocks. Once that has happened you can slowly remove the old rocks without removing too much bacteria at once and the tank will stay cycled.
However, you will want to be testing your ammonia frequently during this process just to make sure that things are going well.