I have 7 socks in rotation that I use. After 3-4 days I remove the dirty one and replace it with a clean one. The dirty sock gets blasted with the garden hose outside and then goes in a bucket with a little bleach. When I'm down to the last sock they go into the washing machine for two cycles(water only no detergent or bleach). First cycle the socks are turned inside out. By the time I'm ready to replace the last sock in the sump the ones that have been washed have been drying for a few days and are fully dried and ready.
In your case without a washing machine I would just make sure to rinse them well and be fully dried before putting it in the sump. Pick up one or two more socks if you find that there isn't enough time for them to dry before having to change out the dirty one.