What you plan on doing sounds more like cloning than actually cycling. Let's say your 20 gallon has 12 guppys. The media can handle the bio load of those 12 fish. You could safely take 1/3 of the media, and 1/3 of the fish, and add them to another tank without any cycling worries. As long as you move the percentage of media and the same percentage of bio load you shouldn't have a problem.
With a community tank that has a mix of fish, it's a guesstimate deal. In a mature tank your nitrifying bacteria can double in about 24 hours. Also, healthy adult fish can easily go for a week without being fed, and less food in means less food produced. What you do is don't feed the fish for 24 hours before, and 24 hours after the move, then feed lightly for the next week. This will give your bio filtration a chance to catch up.
The same goes if you want to start a new tank, with some new fish. Take out a portion of the mature media, but no more than half, knowing the nitrifying bacteria can double in 24 hours. Follow the same fasting & light feeding schedule for both tanks.
This is something I do on a regular basis, starting up & shutting down tanks as my stock varies. I keep spare filters running in mature tanks, and when a tank needs to be set up I pull a filter, and don't feed that tank for a couple of days.