You don't do anything!
Assuming you are not on a remote island, a paramedic will be with you very fast if you have a BBA. You are high priority. They carry all necessary equipment to cut the cord.
At least in my area, they do not, and cannot, administer the injection. All they can do is watch, wait and transfer if there are concerns about blood loss.
The MW, however, can administer the injection even if she misses the birth. They prefer not to, but may on a risk/benefit analysis, in my case that happened as it hadn't shifted in nearly an hour and was showing no signs.
The worst thing you can do in this situation is mess about trying to cut the cord without knowing what you are doing, or (far, far, worse) do anything to 'encourage' the placenta. There is masses of time for it to be dealt with. And if there is excessive blood loss, there is an ambulance on its way!
Have you had a look at Dirty Duncan and Shiny Shultz presentations of placentas? It's basically whether they come out with all the yuck wrapped inside or not. That might explain why they looked very different? Random link from google here