First, she is a beautiful baby...such a precious little thing. I hope all goes well.
Now...I have to play lawyer and give this advice (for what it's worth - your state may be different).
If he doesn't sign to put his name on the birth certificate now, he can always do it later. But, if he does sign now, it is legally a binding declaration of paternity and he will find it VERY hard to contest paternity later if he suspects or find out for sure that he is not the father. Bottom line, if you can prevent it, don't let him sign until you do that DNA test.