I don't think you need paperwork but someone is bound to ask to see the baby at some point
Yep, so a week later when Emo jr is born you return and show a bunch of pics without time stamps then take a few more days vacation.
Also, I took the first three days, went back for two, then took two more, went back for three or four, then took another two, etc.
Between mother-in-laws, sisters, etc, my wife had enough company where she didn't need me 100% of the time, yet I was there enough to help as much as needed and take in the experience. Also let me drag out the process of being there more than just the initial week and because of that it helped my wife phase into what the next 6-8 weeks of maternity leave would be once the family and I were both back to work full time.