If you plan on getting a skimmer, you could get by with a cheaper version for the 20g. Maybe get a skimmer for a 50g+ tank so you can use it on your next tank upgrade?
In my opinion, with a 20g nano, a hang on back skimmer would take up a lot of space. Lots of people go with JBJ or all in one systems where all the "gear" is internal. I have a 30g with hang on back and I think its a major distraction from the tank.
It might be possible to go without a skimmer (I can hear the heckling already.) You would have to make sure you keep up on water changes and have a productive cleanup crew. However, I doubt you would have the ability to keep LPS or SPS corals. Many fish, mushrooms, leathers and certain polyps (if i'm not mistaken) do just fine with tolerable levels of nitrate. You could specifically build your tank knowing that you can only host these species.
Pick your poisons