what is a dry birth

I am a labor doula and have never heard of this.  A birth is never dry (amniotic fluid, vaginal mucous).  Maybe you mean land birth.  A baby that is not born in a birthing tub (water birth).

 If you are concerned that your birth may be dry, don't worry most doctors and midwives use oil mineral or other such as olive to help the vagina, labia and perenium to stretch during crowning.  Birth is anything but dry.