First of all, congrats! Fatherhood, while challenging, is one of the most rewarding experiences in life. I'm a fan.
Secondly, if more than 50% of the recipients of these cigars are NOT regular smokers, then I would say save the cash and spend it on a nicer stick for yourself come the little lady's first birthday. I bought a box of 8-5-8s when my son was born, and half of them didn't even get smoked more than halfway... which was kind of a waste.
Third-ly, if this is your first child, I recommend reading
The-Three-Martini-Playdate. This book really helps put some perspective on how parenting can change your life for the worst.