When I am cleaning a blade to "dry" I use the following process:
1 - Ballistol soaked cloth to wipe off lint/particles/dirt.
2 - Dry(ish), lint free, soft cloth to wipe excess oil. Will replace a few times a year.
3 - "dirty" high grade chamois to remove remaining oil. (will replace once or twice a year)
4 - Soft/lint free clean cloth for dust down/ clean.
5 - high grade clean chamois to dry blade.
6 - Apply Ren wax.
I also use a chamois to wipe down handle and stainless fittings after handling.
For me it is important to use a "wet", "dirty", "clean", "Dry" flow and segregation to avoid contamination and retention of particles which may scratch the surfaces. I keep each stage in separate containers, and only apply a firm pressure in the final stage when I am sure there are no hard particles held on the blade or cleaning materials.
......... yes, I am very weird and extremely picky