Not sure about the mole, but if it can't be removed, you could try plucking the hair instead. The hair would come out by the root so would be much thinner when it grows back.
I am pretty certain it can be removed, you need to go and have a chat with your doctor. Or you may be able to get laser treatment to kill the root of the hair. A beauty salon can do this for you, but before they do, they should ask for a letter of referral from your doctor. Hope this helps, Sue