Well, you CAN run a tank without a skimmer...Fish only especially as fish aren'y quite as impacted by nitrate levels. But there is definitely a benefit to running one, especially if you keep predators. It helps with overall water quality.
You can get by on water changes alone, but a skimmer helps, especially with preventing things like algae problems. I had all sorts - but had living animals - before I got a skimmer. But with one, things improved a lot.
If you only have hang on filters...I would definitely add a skimmer. It will help tremendously, and basically be more effective, IMO, than the filters themselves.