Dissolving sebum (the oily substance that protects and waterproofs our skin) sounds like a neat chemical way of removing it - a way to remove skin oiliness. But the solvents that dissolve sebum in a test tube are likely to be too aggressive for extensive use, or to have an oily nature in themselves.
Of the safe and common solvents that might be useful, isopropanol (91% if available, or 70%) would be somewhat invigorating - if not used in excess. It will almost certainly dry the skin, perhaps too much - so that you resort to applying a skin lotion to provide some oiliness.
An alternate way of removing sebum from skin would be to emulsify it with a detergent. Sodium stearate is a common, safe detergent (actually, a soap) which is somewhat soluble in water and available commercially (Ivory Soap is 99.44% pure!). Applied to a washcloth, it will remove much of surface sebum. Rinse, lather, repeat.
Some chemical and cosmetic improvements have been made to other products: added colors, fragrances and acids to reduce the pH from neutral to slightly acidic, for a gentler action on skin; added water for semi-liquid soap (Soft Soap).