I normally do not change UV sterilizers or protein skimmers when using ionic copper at 0.20 ppm.
My understanding (from when Tom Frakes worked for Aquarium Systems - so at least 15+ years ago) that Sea Cure is simply a copper sulfate / citric acid solution, so my adivce would carry over to it, UNLESS they have changed the formulation since then.
If they take it off the market, it is rather easy to make your own:
4.26 g Copper sulfate penthydrate
0.91 g Citric acid
100 ml deionized water
Initial dose is around 1ml of this solution per 14 gallons of tank volume - but you must confirm this using a good copper test kit.
Jay