My fiancee will be happy to hear that theres no need of filling out an application for her
It would be too stressful on me ,having to fill out a visa application for her as well
The only forms he'll need to fill out/sign are her birth certificate and passport app. She will need her British passport to enter and leave the UK, but the forms are readily avaiable at the post office.
She'll need a 'long form' birth certificate for her American citizenship - from which the US will generate her Certificate of Birth Abroad. There's an extra charge for this, but the Register House when you take her to register her birth can provide them.
The US Consulate or Embassy can post you the appropriate forms before the baby's born so you'll have them all filled out for your appointment - when I had our daughter, I didn't have to take her into the Consulate to swear her oath and put in her papers, but I understand now the child has to be seen in person as well.