Denatured alcohol.. or "methylated spirits" seems to work to remove oils from contacts. After you're done use some "Deoxit" on them. Just a very tiny bit.
Put a little light mineral oil in a very clean tiny glass jar with a tight fitting metal lid (e.g. fish paste jar, or miniature jam pot), add some denatured alcohol and shake it. Let it settle and you will see the oil and alcohol separate into layers. Leave it long enough and the separation will be near complete, maybe with the remains of a homogenised layer of tiny oil droplets in alcohol between the other two layers. That shows you oil is not miscible with short chain alcohols. Shake it again, tip the contents out, rinse with a little more alcohol and let the jar dry and run your finger round the inside. It will still be very oily. That shows you alcohol is poor at removing oils.
It does have SOME cleaning effect combined with vigorous scrubbing or wiping as oil cant stick to a surface wet with alcohol, so it can be used to float the oil contamination away from surfaces that cannot withstand more suitable non-polar solvents (assuming the alcohol is safe for the surface), and if pure Ethanol is used, the intoxicating fumes will be less harmful than those of any alternative organic solvent which can be important for safety when working in confined spaces, but its far from being first choice for oil removal.
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Potentiometers and any switch with sliding contacts needs to be lubricated after cleaning.
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Silicon oil is commonly used also.
One needs to be extremely careful to avoid contaminating moving contacts with silicone greases and oils. Any sparking or arcing will cause the silicone to break down into nanoparticles of silicon dioxide (insulating glass) and silicon carbide (a poor semiconductor and a harsh abrasive) which can cause accelerated wear and an unreliable connection. However its excellent for protecting fixed contact surfaces that are never connected or disconnected or moved under load.
See
The Use of Silicone Materials in Close Proximity of Electrical Motors and Mechanical Relays by Frederic Gubbels / D. Varin / M. Onishi, Dow Corning Corporation
and
Contact Contamination and Arc Interactions - slides by G. J. Witter.
Its also a total PITA to remove silicone contamination from a surface (may be impossible on adsorbent surfaces or without total disassembly), it tends to spread to exactly where you don't want it and trace contamination causes glue bond failures and paint adhesion problems so always think twice before resorting to using any silicone containing product on any valuable equipment.