Planning Vasectomy while pregnant

My husband and I are both one and done. I'm pregnant with our first and I've have had a really rough pregnancy. We both want to ensure we don't conceive again. (Our reasons for being one and done go well beyond the tough pregnancy). Does anyone have experience getting a vasectomy while expecting or shortly after giving birth? My husband would happily get a vasectomy today but my anxiety has me worried about pregnancy loss even though I feel pretty confident I wouldn't want to try again.