This is old debate, I'm really not sure that there is a wrong way.....
I was never worried about bacterial population, when adding, replacing, removing..... from tank, bacterial population will grow very quickly, so, in any larger water volume, bacterial population won't be issue.....
Things that i want to keep are micro fauna, various pods, snails, stars, worms, etc.... I know that the modern approach consider this things as pests, i'm not too convinced, always think that this stuff are part of healthy ecosystem in our tanks. And if things gets out of control, then anything can be considered pests, so, if not harming anything, let it live....
Back to topic, so removing rock looking from point of bacterial population, won't do any harm in your tank. If the new rock who replace old is dry, sterile (as it can be) and clean, really, nothing wrong or unwanted will happen.
Looking from point of removing micro fauna, still, very slim chance that something will actually go wrong, i just don't feel comfortable to reduce part of this population with no real and strong reason.
Also, i'm kinda strange in opinions and views, so, cycled rock for me isn't rock with bacterial population, cycled rock is rock with established micro-macro fauna, desirable algae, coraline..... So in that term, cycling rock in bucket of water is good from point of bacterial population, useless from any other points.
Maybe the safest (mind - not saying the best) way is to put that rock in tank for some time, when life populate that rock, then impact of removing anything will be less... Not crucial, but, why bother to keep separate container for weeks, powerhead, heater...... also, keep in mind, to grow bacterial population, you'll have to feed it, so...... too much hassle with very little gain.
Newer had any issue, maybe it's weird approach, but like i said, for me, tank/rock/sand is not cycled until various life forms don't find way to spread, reproduce and maintain healthy population.