Thanks and glad to see you care about friend..and you need not worry as your friend has just stage one melanoma.
Normally stage 1 melanoma (less than 1mm thick) can be excised with the help of local anaesthetic and its completely safe during pregnancy.Most anaesthetic drugs are safe and won't affect the baby or the pregnancy.
Melanoma spreading to the baby is a very rare.This might occur in pregnant women who have most advanced melanoma spreading to lymph nodes and internal organs.In your friend case its safe.