Most plants aren't in the least affected by H2O2. Java fern and anubias petite, for example, I can remove and spray directly in the sink and let sit for 1/2 hour while cleaning tank and they are not the least bit affected. However, P. Erectus will melt if it gets anywhere near it. I try to keep it away from stem plants.
Try a small sample and wait a week.
A lot of algea will be killed by H2O2, but not all.
It works best to remove plant but not all can be removed. Take a look at Dave's video, I do this with c. parva:
I know its not the "answer", but for some plants, e.g., c. parva and anubia, it does real well.
CVS has a great 4oz spray bottle that can be refilled. Its great for spraying nozzles, powerheads, overflows, etc. when doing water change.