Lamp Gone Gummy

[j44ke]

I have a nice LED desk lamp with a soft-touch surface coating that has gone sticky after 4-5 years of use. The result of any attempt on my part to unstick various pieces of household fuzz has merely clumped and smeared it around. The lamp is tacky to the touch and is starting to look like crap. Any ideas for de-tack-ifying? Pretty sure most of the surfaces are plastic, except for the articulated arm which is metal.

It is a nice lamp, but I'd like it better without the flypaper finish.

Thanks in advance to the VSalon braintrust.