Well, I keep a brand new 3" nylon paintbrush that I've cleaned a few things with.

Use it to dust the radio with first, then rinse it out.

Shake out most of the water and spray with some Simple Green.

Work it into the brush and dry fairly well with a towel and use it to work the corners and crevises. You can kinda control where the small runs are and catch it with the brush. You dont want to soak it where it will run inside the box, of course. Tilt and work upside down if you have to.

Repeat with a clean damp brush.

Wipe everything down after than with a damp towel and you should be good to go.