Disease-free sex between virgins?

Hi there, I had recently gotten a vasectomy and me and my fianc�e are thinking of having intercourse. The thing is, me and her are both disease-free and still virgins. We have been since 2006 (when we first met). Since neither of us have any STD or history of any communicable disease and I am officially sterile, is it okay to have sex without a condom? Again, me and my fianc�e are both virgins, clean of STDs, and are totally healthy. Should I be nervous? :)