I would consult with a cosmetic dermatologist to determine if the mole should be biopsied, or to discuss treatment options for cosmetic removal. Treatment options may include shave removal, excision, or removal by laser. The cost, size of scar, and healing time varies depending on...
This should be shaved all the way down, at least that is how i do it in my practice. I suggest seeing your physician and asking about his/her long term plan. Best, Dr. Emer.
Moles will regrow if you decide to partially remove them. If you are concerned please have it completely removed by a cosmetic dermatologist. Best, Dr. Emer.