While I laud your desire to have a 'natural' tank - as you're seeing - it's quite difficult - especially with higher stocking density/large fish. A 'natural tank' also has multiple definitions. IMHO - to specifically answer your question - a UV will first kill bacteria, in the tank - with larger units - it can help keep down the number of parasites - though there is a little debate as to how effective this actually is. So if your idea is to have many/all of the bacteria 'in the ocean' in your tank - a UV will dramatically change this. That said - I'm not sure there is a lot of good data out there suggesting that it's possible to have anything close to those levels in ANY reef tank.
If you are going to treat all of your fish (with copper in a hospital tank) - for 30 days, you may want to add 2 prazipro treatments 8 days apart - per the protocol at the top of the forum. This alone should remove all of the parasites from the fish - and the fallow period will remove them from the tank. You would then need to treat any new fish in the same manner - before adding to your tank.
There is nothing 'un-natural' about a protein skimmer IMHO. The balancing act with the type of tank you're attempting, is that most fish do best (with illness, etc) - with pristine water conditions - and not using some of the equipment makes that more difficult.
Best of luck - and sorry about your fish!!
@atoll may have some words of wisdom