I joke that my having my son turned me into a man...
While I never had any need before I now get the "full face" (lip, cheek, jaw, sideburn, chin) waxing at Gene Juarez every other month.
If it's just dark downy fuzz (and not the skin itself that's darker) waxing will take care of it. And if you ever actually LOOK at the waxing menu, you'll realize that...yup...we quite literally get hair removed from every single part of our face (and bodies).
If it's the skin, a trip to the dermatologist can stand you in good stead. While it may very well self resolve when you stop nursing (ugh, stupid hormones), if it doesn't they can actually bleach the skin back to matching with the rest of your face.
Good Luck, What we suffer for our wee ones.