Simply massage on cold pressed oil (almond, sesame and coconut are great) into your face with gentle upward strokes, then gently towel it off. Your face will be incredibly soft and not the slightest bit oily.
Just tried your idea but the whole experience left me somewhat frazzled!
First the coconut oil had melted in the heat, only realised this upon opening the jar and spilling it all over the bathroom floor. Put coconut all over my face, too lazy to get wash-cloth from bedroom, so just got in the shower and tried to rinse it off with my hands – it was like basting a chicken in fat.
Got out of shower dripping water all over wooden floor in hall, went to bedroom for wash-cloth. Slipped on wet floor on way back to bathroom and hurt leg.
Got back to bathroom to find I had left shower on. Drain blocked and water overflowing.
Cleared up mess and was late for work.
p.s. oh yes, besides the problems, it worked well.