Back a long time ago I had a bunch of HT1000's to get rid of. They needed to be cleaned up before I sold them. Here's what I used:
Denatured alcohol. Works well on plastics. Often sold as a "plastic cleaner". Wetting a rag or paper towel and wiping down the radio removes grease, oils and dirt. Works really well at removing adhesive residue from labels, stickers, etc.
Compressed air works well for cleaning out dust from under controls, audio ports, etc. Small cans of compressed air for cleaning computers can be purchased for a few bucks. If you are going to use an air compressor, turn the pressure way down or you can force dust into places you don't want it, like behind screens.
Soft toothbrush works well for working loose more stubborn dirt/dust. Small paintbrushes work too.
Armor-All does a great job shining the radio up. It made the HT1000's look almost new. As stated, it can attract dust, but if you wipe the excess of really well, it's usually not an issue.
All that worked well on radios designed to take quite a bit more abuse than a scanner is, so you'd have to be careful. I still keep denatured alcohol in my shop for cleaning, as well as a few old toothbrushes.
Being really careful with the screens is key. On the consumer stuff, they aren't always sealed well, and forcing dust behind them is a risk. Same with any fluids, don't spray directly on the screen, use a damp cloth, microfiber, as Lou suggested, but be cautious as some screens scratch easily.