Don't worry, the only bloody part that was filmed was the baby laying on my stomach, none of the actual coming out, I'd never watch it again let alone let anybody else watch it.
Funny, that kind of thing never did bother me, even before I did it myself...suppose I'm weird or something.
Most guys who are in the labor room with their lady do not see most of it. They are busy being close to their lady and holding her hand. It is not like they are down there catching the baby. (Though some places do give you that option.)
The local hospital does give that option...and every now and then they have to pick a guy up from the floor after he passes out.