Can I do it?

I am a very firm believer in large water changes weekly for stability in Nano tanks.  Just my experience.  My BioCube 29 had a refugium mod with a cheato ball (that grew and I gave it away) as well as a AquaticLife mini skimmer etc.  If I did NOT change 4 gallons a week it would be obvious that things were going down hill within the next week and I only every went longer than 2 weeks and paid for it.  I sorta figure that clean fresh water mixed to exactly the same salinity is a very good way of "supplementing" a nano... there is no other system you can find that reasonably can get meaningful alkalinity etc by a water change... but 20% weekly in a nano will do this to some extent.  It got to the point where I was excited to do a water change, everything (and I mean EVERYTHING) would just perk up and look so much better as well as crystal clear water.

You DO need to supplement as well.... but at least consider the water changes or go without and see how things do... its also a great nutrient export solution...  just my 2c experience with a single tank.  I can no longer accomplish this as I now have over 80 gallons of water (no way am I mixing 16 gallons a week).  But I now rely upon much more efficient export apparatus such as a high performance skimmer a much larger refugium with a sand bed etc etc... 

I guess part of why I did this was bioload, I had 4 fish... and without water changes it was obvious that algae was going to be an issue if I choose to feed a lot (and I do) so there are many ways to keep a nano... 

Activated carbon is goooodness.

Change it often, its cheap and you need so little in a nano its not worth letting it go too long between changes.