If you are really cycling and that means you have ammonia and subsequently nitrite spikes than you
normally don't do water changes. Exception would be that you would like to preserve some life on the liverock and don't want to get ammonia/nitrite over a certain threshhold. But that's not that what's normally meant with cycling. Every dilution of the ammonia/nitrite laden water prolongs the process of cycling and could spark mini-cycles afterwards.
But if you get cured liverock directly into your tank you won't start a real cycle in that sense.
(Just watch out that the water has already the proper temperature when adding the liverock. I bought my first liverock in November when the pre-mixed RO water that I bought together with the liverock was already 11°C cold and the boot of my car had around the same temperature. What left me only two choices: leave the liverock without water or put it into the cold water. I did the last one. On that liverock survived only a strain of Chaetomorpha. My first stupid error ...
)
Generally, it's been said that on a nano you do at least 10% weekly water changes. I do almost 20% weekly and that is often not enough due to overfeeding.
The water changes
can compensate the use of a skimmer. If you start without livestock that is not an issue. You can change less or less often.
Also, it depends on the bioload of your tank. Grossly simplifiying: the more food enters the system the more nutrients you need to export to avoid pollution.
A skimmer removes nutrients constantly without water changes. How much skimming or if at all you need depends on the amount of food and the size and number of livestock.
Water changes are necessary with a skimmer, too, but not that much. That's the reason because mainly larger tanks go only with the necessary water changes to restore used up calcium and other elements and do the nutrients export mostly with a skimmer. What you pay on the skimmer in advance you'll save on salt later.
In a nano, the more frequent water changes don't cost that much, are easier to perform, and a skimmer
can be left out.
But all depends on stocking. Many people do on a pico water changes twice a week. I am fine doing it weekly because the corals and the only hermit don't eat that much and don't pollute the system as much as many people squeeze even in a pico a little fish and dozens of corals.