I haven't heard of peroxide being used for aptasia. If you want to give it a shot I would remove the rock if you can and place it in a container with tank water and some peroxide and let it sit for a few minutes, that's what I've done before with some frags that had algae on them.
For killing aptasia I've heard of injecting them with boiling water, lemon juice or vinegar or one of the store bought ones like Aptasia-X. The problem with those is they can make it worse like in my case. I used Aptasia-X and although it worked for some ( big ones out in the open ), the ones in the holes and crevices it just made them retract and come back in numbers. When I first started noticing Aptasia in my tank I tried Peppermint but they didn't last long with my Wrasse. I bought a Copper Band Butterfly last year and it looked like he was eating them for a while but stopped. Throughout all this I was using Aptasia-X and that has caused the infestation I have now. My last resort is Berghia Nudibranch and put some in my tank 2 weeks ago. They are expensive and I was worried about my Wrasse making an expensive snack out of them, but the Wrasse is buried in the sand before the lights go out and the Berghia do their thing at night so the chances of them running into each other is very slim. It will take a couple of months to see if they worked.
