Back in the day when I would get done honing a block, I would always wiped down the bores with a lint free thinner soaked cloth ( cloth baby diapers were perfect). Doing this removed any fine metal shavings from the cross hatch pattern.
we washed it with soap and water then wiped with wd40 and clean rags until they came out clean.. amazing how much dirt stays in there. it will get wiped down again before assembly.