There is a fair amount of anecdotal information that indicates that noise can cause fetal movement. My step-daughter, the the third-trimester, attended a Southern Baptist Funeral Service. The shouting of the triumvirate of preachers was enough to cause the baby to kick in earnest.
I am unaware of any focused studies conducted on this subject. Doctors, especially in this litigous society, will answer no to almost anything that hasn't been studied to death.
That said, I would go with shooting outdoors, using the .22 (in as long a barrel as one can), and a suppressor if affordable.
As to lead, it's not going to zero in on you because one is pregnant. Airborne lead, even in a properly ventilated indoor range, isn't going to be a problem. I mean, if the nanny-state allows it, with all of it's anti-gun helpers, there isn't much of a risk. Lead on your hands and face is a larger, but still minor, threat. Wash you hands and face before eating or drinking is good advice for anyone, not just pregnant women.
To keep the fetus safe, one should, ideally, remain in bed, waited on hand and foot, for the entire gestation period. You need to be monitored medically that entire time, as well.
OR, one could use good sense, and have a perfectly healthy child. If one believes that noise may adversely affect their unborn, then, for peace of mind, noise should be moderated. Walking past a jack-hammer on the street, or a loud car, or loud music, are other examples of noise pollution that we can't always avoid.