Try using a spray-bottle with distilled water first. Just spray the bejeezus out of the mold until it flattens to the point where you can hardly see it. After that, and grown well, it may not come back. (Anecdotal. That's how I've dealt with minor infestations, and it's worked in the past.)
For peroxide, you could try 2 tsp. 3% peroxide solution to 1 cup of water. May or may not be enough to kill the fungus, but that ratio hasn't hurt my sphagnum. I would definitely want to be able to drain / flush that if I were going to treat very much of it, though. I've only used it on sphag that's potted along with plants, so it doesn't really have a chance to sit for long.