I am imagining you haven't quite taken the trip yet, since it's still just spring.
Ordinarily, I also would be shy about leaving an airport for only a little time, but CPH is not so far from the city and well connected by the metro, which is driverless. There is usually no reason to rush to a metro here if you are at the top of the steps because another will come in literally two minutes. I'm assuming your layover does not have special circumstances (like at 2am on a Sunday night). My experience at CPH has never been like what it is in the states.
The metro from the airport to Kongens Nytorv, for example, will take you 13 minutes. Norreport station will take you 15 minutes. Both would be great places for you to peek out at Copenhagen for a few hours and it would be really straightforward to get back.
I got those times from here:
http://www.rejseplanen.dk/bin/query.exe/en?ml=m&
If it redirects you to a Danish part, it is written in English.
For so short a time, it will make your life easier if you change your money, a little bit, before hand. Many places here ONLY take a Danish credit card with a chip in it or cash, this is particularly true at grocery stores: if you don't have cash, forget it.
Be warned: it is unbelievably expensive here. I thought London at the height of the pound was expensive. Nope. But if you like them at all, the hot dog stands are absolutely a Copenhagen/Danish thing and not to be missed.