Once the cycle is complete, it is best to do a large water change to help reduce the excess nitrates but since you do not have any really, a regular water change would still help replenish the trace elements depending on the cycle time frame. It gets the chemistry up to par in preparation for possible animal additions.
The skimmer will not get much from the tank unless using uncured LR
to cycle with. You can really forgo the skimmer for the first few weeks at least since there may not be much DOC
at this point. It will allow an opportunity for coralline to get hold and spread if the lights and chem are good.