I have set up several tanks in the last 12 years I've been in the hobby. I don't cycle tanks with the skimmer on, nor with live animals. For the last 4 tanks I did not use live rock, or live sand for that matter. I add nitrifying bacteria and ammonia, which guarantees my system has a lot of bacteria to start with and a measurable amount of ammonia from day 1. Before bacteria in a bottle I used live rock and a dead shrimp. The way you are doing it works as well, I assume you plan on keeping the damsels. My reasoning behind not running the skimmer is because you do not want to remove bacteria, you can always remove the gunk once you are done cycling. The marine biologists who sell the bacteria say not to run it for that same reason. If you are worried about the PH, you can run the skimmer with the exhaust all the way open, like that nothing beneficial will be removed and the aeration happens. Though plenty of tanks dont run skimmers at all and they do fine.
There are plenty of cycling methods, and lots of opinions as well. My only advice for anything is to research as much as you can, get all the facts, and go with the plan that makes more sense to you, but do it in advance. It will keep your critters healthy and save you money in the long run.