For this you'll need a dermatologic surgeon (sometimes called a "Mohs" surgeon)  or a plastic surgeon.   And yes, you are always trading a mole for a small scar.  It's just a question of making very sure it's a good trade.  The upper lip and the nose especially are tough areas to get a good result because there isn't as much skin to work with and you don't want to change the contour of either. 

 Whether a shave (taking flat with the skin - no stitches) or an excision (with stitches), is done depends on many factors like the size of the mole, the type of mole (more flat or more raised), the exact location on the upper lip, whether you want hair growing out of it removed too, etc........

 Costs are generally less for this in a dermatologist's office but not always.  Remember that if the mole is normal clinically, your medical insurance is unlikely to cover the removal.