The only way I would run a skimmer during a cycle is if you are curing live rock. If you have live rock and are cycling with something else then I would not run skimmer . Wait until ammonia and nitrites are zero then it would be ok to run skimmer, . skimmer will only prolong cycle by removing to many good nutrients that are essential to a good cycle.
During my cycle, i turned on the skimmer 2 weeks within when my nitrites were peaked and the nitrates were high. They both dropped to 0 in 3 days. Im sure it was the skimmer.