I used to.... gosh, still do, have this problem with my N90S. Not on the grip so much as on the camera back. Like you, I have always been meticulous about keeping my gear clean so this problem has always perplexed me.
And, lately, I've noticed that my D7000 sometimes feels a bit sticky after a day of use. I'm guessing the culprit in both cases is skin oil.
On the N90S I've tried plain dish soap and water (very small amount of soap) and just plain distilled water to no effect. Like you, I'm afraid to use harsh chemicals or alcohol.
Hopefully, someone here has figured this problem out.