My mother (almost 60 now; didnt did any manicure nor hair dye when she was pregnant with me), but I was born with half my face black birthmark too. So I dont entirely believe it'll affect.
My husband's cousin pregnant with her 3rd child now, always doing manicure & hair dye, her 2 sons no birthmarks. Just sharing~
I undergone face lasik since I was 3 years old, yearly once or twice till I was 18. The birthmark is totally gone on my face (but no under the sun sports, I have been avoiding sun since young due to face lasik).