Removing thread algae (Rhizoclonium?) from driftwood

Hello folks,

I took down a 20 gallon long tank this evening, after it became quite infested with what I believe is Rhizoclonium (long green strings that can form into a ball/mat, almost like wet hair). I have three small pieces of driftwood that are also fairly covered with it. What is the safest way to remove the algae from it, so I can return it to my RCS tank ? I have read about bleaching it or using peroxide, but I am afraid of bleach leeching into the wood. I've read that a bleach solution should be 5-10% bleach, but I'm not sure about peroxide.

Thank you.