Is it safe to do electrolysis while pregnant?

Yes: The reaction appears local and should have no effect upon a pregnancy.

Difficult question: There are really no studies looking at the safety of electrolysis during pregnancy. Theoretically it is possible for the electrical current to stimulate muscle contraction if the needles are inserted too deep. But uterine muscle is intra-abdominal and a low risk target. I would suggest you use waxing until your pregnancy is over. I would also recommend you talk about this with your ob.