I wouldn't worry about trace elements being depleted by carbon. I've read several comments from RHF on the other board, in which he stated that the amount of trace elements taken out by carbon is negligible.
Google: Ozone and the Reef Aquarium, Part 2:
Despite their widespread use with ozone, skimmers are not usually an optimal way to employ ozone for several reasons:
1. Their water and air flow rates, and even their engineering design itself, are optimized for skimming, not for ozone injection and reaction. The longer the ozonated water has to react, the more oxidation of organic molecules can take place. This is not a design criterion with skimmers, where the air/water contact time is maximized, but the water alone is not held for any purpose. If the water's flow rate is too high, and hence its turnover rate too high, the concentration of ozone in the water, and the contact time for it to react with organic materials, may be less than optimal.
2. Both the air and water exiting the skimmer should optimally be passed over activated carbon to reduce the highly oxidizing and toxic species being sent into the aquarium and into the aquarists' home air. Many skimmers are not set up to efficiently pass the air over carbon, and high water flow rates can make it difficult to achieve adequate contact with activated carbon.
3. Many skimmers are not designed using materials suitable for prolonged ozone exposure.