For the bleach step, you're just killing the mold, not cleaning. Use a sponge to apply the solution to the vinyl. If you have a MOFI or DD brush you don't mind possible destroying, it would be useful to ensure penetration of the solution into the grooves. A very soft toothbrush will also work. Apply the solution with a sponge. Use the brush to gently swish the solution down into the grooves. (Water surface tension may otherwise prevent the fluid from getting into the grooves.)
I would set this operation up at a kitchen sink. Lay out a cloth on which to place the record.
Use a second sponge for the rinse step. Since you will wash each of your LPs later with a good record cleaning fluids process, I wouldn't get too concerned at this stage other than to rinse reasonably well, but not be fanatical about it.
Be aware that the bleach solution and the water rinse will be harmful to the labels. But you will want to ensure there is no live mold residue left on the labels or hiding in the center hole.
When rinsed, lean the LPs upright in some fashion to allow each to dry thoroughly. I lay a towel on the floor along the edge of a wall and then stand the LP on the towel and allow to lean just touching the top edge at the wall.
When dry, stack between paper towels until you can clean them. Go next to cleaning the record jackets with a similar bleach solution and allow the jackets to dry thoroughly. Throw away the inner sleeves. Then move on to cleaning the LPs, insert in new inner sleeves (as you stated earlier you plan to do) and insert in the cleaned and now dry jackets.
I would follow exactly this same process with the CDs. Soap and water will not kill the mold. It may successfully remove it, but I'd want to make sure I killed the mold, and then clean the CD.
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