Really, you want to rinse your surfactant out of your clothes. There's not much point in making an emulsion of your grease, then leaving it there till the surfactant evaporates. You want to emulsify the grease to render it water-dispersable, then disperse it in water, then remove the water as a liquid, then let the remaining water evaporate. To clean anything the surfactant has to leave in the aqueous/liquid phase of the cleaning solution. The use of a volatile surfactant would be to suspend an oily substance in water, and then leave it behind when the water/surfactant evaporate.
If you just want to wash out an oily substance without water, then as in dry cleaning, you just need a solvent, not a surfactant (and still want to remove it in the liquid phase). So if you want to clean a greasy stain, add the solvent, then blot it off. Acetone (or the previously mentioned isopropyl alcohol) would probably work well, with the stuff you don't blot off easily evaporating (or coming out in water).