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Soapy warm water and a soft-bristled brush?

This method safely cleans original paintings and should work on the lamp also. Wipe it gently with cheap white bread, then brush with a natural hair paintbrush.

Go to an art supply store. They have all kinds of things for cleaning fragile surfaces. My first thought for you would be a cannister of pressurized air that remove dust without any abrasion to the surface. But there may be something even better.

P.S. I wouldn't use anything wet.

I'd use warm water with Murphy's Oil Soap, with a soft cloth, using as little moisture as possible to do the job. Cork is a tree bark, so what works for wood should work for cork, although I wouldn't use anything lemon-oily or waxy.

if your cork is untreated it's probably more like the cork on a flyfishing rod then a modern cork floor. i'd try denatured alcohol and then soapy water if a second cleaning was needed. let it dry between methods.

also, the alcohol can effect the patina/color so try it on the bottom first if you are wedded to the current tone.

I once used liquid hand sanitizer (which contains alcohol) in a pinch to clean a pair of cork wedge sandals. It actually worked really well!

I own the same lamp in the picture above, and what worked wonders for me was a Magic Eraser (I mean what doesn't it clean honestly?).

It didn't harm the Cork, nor did it make it too moist. Worked like a champ without chemicals or sprays!

Fine sandpaper. Just saying. I've used it with good results for cork objects, but of course it will remove any "patina," or sealer if there is any. Depends on what kind of result you want. Next time I'll try the magic eraser sponge though, as per sarahrae above.

I've used kneaded erasers (http://en.wikipedia.org/wiki/Kneaded_eraser) to clean vintage cork-soled shoes, and they do a good job as long as you keep using clean areas - so a big lamp would need a few erasers. Luckily, they're not expensive and are great for cleaning many many other things too (leather gloves, light-coloured leather anything) and they're great for shaping and poking into small areas to clean things too. I'd say first go over the lamp with a clean paintbrush to lift the loose dust away (or vacuum carefully with your brush attachment or some cloth over the end of the crevice tool) and then use the eraser after. Seconding denatured alcohol, if a test provides the result that you like after testing, it evaporates so quickly that it shouldn't disturb any adhesive. You can buy cork sealer in a fishing supply store (for rods) that will give it a finish that is easier to wipe down (great for shoes) - but it may change the appearance, so test that too.

Hi Bob:
If it's just accumulated dust in the nooks and crannies, I found that a quick blast of canned air worked wonders on my cork lamp!

Good luck!

A reverse from the canned air but likely similar in results, I use my vacuum attachment with the hairy bristles to clean my cork lamps, bowl and pencil /pen holder. It gets the dust out of the nooks and crannies and sucks it right up.