Best way to get rid of rust in a blind tapped hole?

As a result of the apartment flood, I've got some steel speaker stands that need work. Rust has formed on the flat surfaces of the bottom. I can sand that out and paint it easily enough. But there are also blind tapped holes under there for the feet to screw into, and those have also rusted.

What's the best way to get rid of that rust?

Maybe I should also mention these things are both heavy and unwieldy, so anything that involves a lot of manhandling, etc., is probably a nonstarter.