If you are going to take unpaid paternity leave and this is your first child I would go down the ignorance route. Treat the whole thing as an "unexpected" medical emergency where you have to take time off because your wife/partner needs you. You can do this with little notice and if you plan ahead you can turn the whole thing to your advantage by making the effort to make sure everything continues in your absence. Check in, send lots of baby photos, and don't let the team down and you will look like a hero.