When I upgrade I transfer the live stock and rock to a holding tank or big trash can while I set up the new one once I have plumbing, sand added, equipment installed (essential stuff), filled with salt water I start transferring the old rock into the new tank and get the aquascape done. Then start adding the livestock. The old rock should not have much of a problem cycling the ammonia so it's safe. I've done this many times:
In the holding tank I separate the rocks and live stock. I put only a few rocks in with the fish and stuff. Make sure you have some flow, a pump or powerhead and a air stone can help too.
If you are getting Pukani dry rock then you should cure it in RO/DI and some bleach. BRS demonstrated that bleach does a good job of oxidizing the organics off the rock. Change the water bleach every week or few days. Should be ok to add after 30 days cureing and then a week drying in the sun. Won't create a ammonia spike but probably will get a nutrient spike so have GFO/carbon handy or some other extra nutrient control.
Good luck