Medical Deduction

No.  The IRS would probably not see such hair removal treatment as improving a deformity (e.g., breast reconstruction after a mastectomy).

"Generally, you can't include in medical expenses the amount you pay for cosmetic surgery. This includes any procedure that is directed at improving the patient's appearance and doesn't meaningfully promote the proper function of the body or prevent or treat illness or disease. 

You generally can't include in medical expenses the amount you pay for procedures such as face lifts, hair transplants, hair removal (electrolysis), and liposuction. 

You can include in medical expenses the amount you pay for cosmetic surgery if it is necessary to improve a deformity arising from, or directly related to, a congenital abnormality, a personal injury resulting from an accident or trauma, or a disfiguring disease."

IRS Pub. 502 - Medical and Dental Expenses (pg. 15)