The cord is not anything to be too worried about. I think a mw once mentioned that 1 in 4 have this. It can even be wrapped a couple of times in many cases. What they look for is how tight it is. The typical cord is 21" long (some longer, some shorter). When the baby crowns, a mw will feel around the neck for how tight it is. If there is a concern (and there is usually not) they will clamp and cut right away, as you suggested. This is what they did with my first born. It all happened before I knew what they were doing. Some cords are wrapped around the neck so loosely that Ina May Gaskin suggests just pulling the loop open and letting the body birth through it to lift the baby up - so there can be a lot of leeway there. Don't worry about it - like you said, you two don't need any more stress.
Mandi - Doula/Childbirth Educator, Loving my DH, DS, DD, DD, missing my three (last m/c 4/2010)