Yeah, it should be fine. If you wanted to be extra safe you could rinse with rodi or saltwater after you did the peroxide rinse or dip if you go that route before putting it back in the tank.
I’ve dipped my corals and some smaller pieces of live rock that had bubble algae in peroxide, but I don’t have zoa’s so I don’t know how they react to peroxide. May want to google peroxide and zoas before you did, but if you are just going to spot rinse with the peroxide you should be fine. If the rock is small enough, you could just dip the rock in a mixture of saltwater and peroxide.
Here’s what a search provided…
peroxide dip is a method to remove algae and pests from corals, primarily used on hardy LPS and soft corals, using a dilute solution of 3% hydrogen peroxide and tank water. A common ratio is 10:1 (tank water to peroxide) for a 20-second dip, or a slightly stronger 4:1 ratio for 20-60 seconds for more stubborn issues, but sensitive corals should not be dipped. It's crucial to use the correct dilution to avoid harming the coral tissue
As for the shrimp and goby problem, they likely would move or may wait for you to put the rock back and remake their burrow.
If you wanted to tackle it in tank, put a siphon hose as close to the algae spot as possible and try your best to suck up all the bubbles as they are scraped lose from the rock