Regular ATF, cut with a touch of mineral spirits avoids any possibility of rust. If I need a bit of polish, I add some ceramic pointy things I got out of an industrial deburring unit that was going to the scrap heap years ago, but, I'm told steel shot works well, also.
I rinse in mineral spirits or kerosene, and let it dry on a rag.
Compressed air, along with a good vise, is the foundation of a workshop.

Best,
Ted