Skimmers are useful in reducing the organic waste and decaying food in your water. Nitrate reduction is usually best done with frequent water changes and some sort of algae that feeds off of it.
If a person is having a high nitrate issue the best thing to do is 1 - find & remedy the cause and 2 - do water changes to reduce the nitrate (which works much faster than a skimmer will)
Skimmers remove wastes which would eventually produce nitrates. Assuming you had no other form of nitrate export (algae, water changes, clams, etc), your nitrates would not be reduced using a skimmer.