Just run your lights as if the tank was up and running normally, and the tank is already cycled. Also run all pumps, skimmers and power heads as if the tank was already cycled. There will be adequate nutrients for your tank to cycle with out letting organisms die intentionally to feed the cycle. Your diatom algae will go most likely go away on its own without any thing needing to be done by you. Diatom algae, and even green algae and cyano algae are typical in nearly all newly established tanks. Recurrence of these algae problems after your tank becomes established however is a sign of poor maintenance or bad feeding habits and these result in nutrient problems. These problems can be handled through normal nutrient exportation.
Safe and sane cycling that will keep your fish and all or nearly all the life that came on, in and with your live rock alive.
Make sure you have a new, good ammonia test kit. Test the tank at least twice a day (morning and evening). As soon as the level gets above one part per million, change enough water to bring it down to safe levels. For example, if your test shows that you're at 1.25ppm, you'll need do approximately a 25% water change to get it below 1ppm. It may take 4 to 7 days or more of water changes until the tank cycles.