For a tank of that size, I suggest ditching both the skimmer and the filter. Rely on the natural filtration that your live rock provides and do weekly 15% water changes.
My most successful reef tank was an 18 gallon that I ran completely equipment-less other than a vortech pump and heater. The coral looked amazoing compared to when I had a 20 gallon tank i had with the works i.e. skimmer, sump, phosban reactor, fuge, etc.
If you have the skimmer keep it, it will not hurt. Skimmers remove dissolved organic compounds, many of which can turn in to nitrate, or phosphate if allowed to remain in the system.
Any mechanical filter, will build up detritus and if not cleaned / changed regularly and often will become a nitrate factory. That is why people generally do not use them with salt water tanks, high cost to replace the filter cartage every 2-3 days. Filter socks are about the only easy / quick mechanical filter that are generally accepted with reef tanks. Many people do not like them because you have to wash them at some point, and they get messy, smelly, and it is an extra chore. Not to mention some people really do not want them in their washer!
That said if you do not have a method to remove the detritus, it will release nitrates, and phosphates it just happens faster in most mechanical filters (unless they are changed often). The goal is to avoid adding any excess of food to prevent adding to the issue, remove what you can (filter socks, skimmer, ...), export what you can(Fuge, ATS, ...), and the rest has to be removed via water changes. The less you are able to remove / export the more water you have to change, with more frequency.