Cord clamping

Amanda • Baby 1 born June 10, 2016 Baby 2 due mid-March 2017 😊
I was wanting to do a delayed cord clamping. I asked my OB about it and she said they'd have to keep the baby at my vagina for 3-5 minutes to get the blood instead of placing him directly on my chest so that he can get the blood. I don't like that idea since I want to hold him right away, but I also want the benefits to delayed clamping. Is there a way to do this?
Has anyone done delayed cord clamping while also getting immediate skin to skin before?