I had a cork drawer that didn't put a hole in the cork. Even sanitized, the used corks were the first to leak or get moldy. Make a bulletin board, coasters, and trivets with used corks. Make a New Year's Eve wreath. Similarly, used bottle caps were the first to leak or rust. Further, don't try to make a meal out of the marinated meat, raisins, and spices after you have made cock ale. It's compost time. Re-use is an admirable concept, but eventually you come to the point where recycling is the thing to do.
My wine bottling procedure is to clean and de-label in a separate session. Soak 5 at a time in the sink with PBW. Take one out, put one in. Scrape label with single-edge razor blade. Take off any remaining glue with a copper or scrubby pad, rinse, put in plastic tub that holds about 15 bottles for handling.
Bottling day, count out new corks into plastic container with sealing lid, add a teaspoon of Potassium metabisulfite and half fill with warm water, shake and set aside, shake again when you think of it. Then put a gallon or so of water and two tablespoons potassium metabisulfite (no-rinse) in one side of the sink. Use two bottle rinsers/vinators to rinse the bottles. This speeds things up. Fill bottles with clear, stabilized wine, pull corks from container as needed. Rinse the two tubs with the sink spray, put aside to dry, then capsuling, labels, and cool dark storage with the bottles laying down to keep the corks moist.