Can I re-pot a Christmas cactus with all new dirt, essentially bare-root it?

I have a small Christmas cactus that needs repotting. Only it has a white mold all over the topsoil. A 1:20 solution of H2O2 only slowed the growth and I didn't want to risk burning it with a low level bleach solution. Scraping the top layer of soil won't work in this case either. I'd like to strip all the dirt away and re-pot it in a mix of fresh soil. Can you essentially take the plant down to the bare root and re-pot it with no detriment to the plant?