Only after it is dry. Mixing bleach with acid makes chlorine gas. If the sock is dry it won't be enough to notice. If the sock is wet with bleach it might be a real bad idea.
I don't know why the aversion to bleach. You guys know that between bleach and peroxide, the peroxide is the more potent oxidizer. That's like saying diesel fuel is too flammable so we are going to use gasoline instead.
Seriously though, once it dries out the bleach will be gone. Sodium hypochlorite is only stable in solution. When it dries it disproportionates to chlorate and chlorine. Since the chlorine is a gas and goes away, the whole thing eventually end up going that way.