Well, you can probably do without either and be fine. A UV-sterilizer has some value in a small tank like yours. In order for a UV-sterilizer to be effective, the waterflow through it has to be in accordance with the manufacturer's rating, which is called "dwell." If it goes any faster, the algaes or pathogens that pass through it won't be exposed to the effect of the bulb long enough to be killed. The problem though, is that not all the pathogens will pass through the sterilizer because there are places in a reef where they would wind up, like in crevices in the rockwork, the substrate, etc. In a smaller tank like a nano, maybe the odds are higher than in a bigger tank that pathogens would go through. Also, micro-algaes are controlled with the use of a UV but only the suspended kind that lead to cloudiness and that's not a very common problem in reefs.
Ozone is effective for clarifying water and "polishing" it so it's crystal clear. They also are effective in reducing nitrates. They're a bit more cumbersome than small UV's but they can be managed.
I'd let your nano run with the water changes like suggested already. If you have a problem with nitrates over the long run it can be addressed with other methods. But, I'd recommend that you get a good protein skimmer now instead of either the UV or ozone and the odds of any problems would be greatly reduced.