Haven't seen the video, but the first song that comes to mind is Weird Al's "Like a Surgeon"...
If that's not apropriate, would a classical piece work for it...no words, but some sort of BGM.
Can't think of the titles, but a song from Stevie Wonder, and another from Amy Grant may work. I think the Amy Grant song is "Baby, baby" and although it sounds like a couple's song, supposedly it was for her first child.
Like I said, I hadn't seen the video, but thought I'd barnstorm...sorry, brainstorm...a bit for ya...good luck!