I don't know about your skimmer but mine comes with an ozone resistant tubing made just for using ozone. Ozone tends to break down regular plastics. After ozone passes through the skimmer it is also wise to send the output through some carbon as well.
Ozone is highly interactive and as a result it needs to be used with special equipment. Any tubing that it passes through needs to be of silicon, which does not interact with ozone. If regular airline tubing is used, it will become hard and brittle quite quickly when exposed to ozone. Similarly, most plastics will become brittle and crack when exposed to ozone so be careful when choosing a vessel for introducing ozone. Ozone also breaks down quickly when exposed to high humidity so it is best to run the air going into the ozonizer through an air drier. This will dramatically increase the production of ozone.
Thomas