From the Microscopy List Server:

I've always cleaned mine using diamond polishing compound. Since we are a metallographic laboratory, we have the polishing materials readily available. I use a 3-micron diamond solution with a cloth or felt pad. With the tip of my finger I swirl the aperture on the pad until the deposits are gone. This is somewhat risky, as an aperture corner can catch and fold onto itself. But this hasn't happened to me yet in the 15 years I've been doing this. I was introduced to this technique by Ken Converse of Quality Images.

Service techs are taught to hold one end of the aperture and use a Q-tip with diamond solution, rubbing in one direction only, away from where you're holding it. This polishes the aperture strip without the danger of folding.

A very simple way to clean almost all types of apertures (except thin foil gold self cleaning) is to polish them with 1µ diamond paste.

I prefer a cut-knap polishing cloth, but even a woven lint-free cloth will do. The 1µ diamond compound should be silicone-free (SPI meets this requirement, according to the late Chuck Garber, although many or most metallographic pastes have silicones). Place some diamond compound on the polishing cloth, place the aperture (or aperture strip) on the diamond, put your finger on it and start moving it in circles. When the first side is clean, flip it over and polish the other side. Ultrasonicate in hot water and Joy dishwashing liquid, rinse (tap water will suffice, although distilled is better) and blow dry with a duster or very clean compressed air, so there are no water spots.

Apertures can last decades. I've even taken apertures that had been overheated in an evaporator and didn't work, and made them whole again. Evaporator cleaning causes the metal to change its crystal structure and often after about 5-6 cleanings, the aperture is no good any more. Polishing will smear any distinct grain boundaries and make the aperture good again.