fibroid -third stage management

I am 37 weeks with a 6 cm subserosal fibroid which has been very low down blocking my cervix and only last week found out that it has moved and that I can give birth at least vaginally if not entirely naturally. (hurray!)

I hate to now shift the goal posts because this is such a relief but...

I have seen very few midwives throughout the pregnancy because of this and also I have had gestational diabetes (has been diet controlled and practically discounted now by endo team as an issue at all). The midwife I did get to see last week suggested I could do everything naturally, today I saw the obstetrician again and she is very keen I should have a managed 3rd stage I don't want to split hairs or take any silly risks- I know its a long way from being sliced open but having got this far I really would like to let nature take its course and let the cord stop pulsing naturally which I won?t be able to do if they give me syntocinon etc...

Any thoughts How big is the risk of haemmorhage, how easy is it to manage if it shows signs of occurring, would it be better to just accept it and be on the safe side? I know the rest of the birth gets to happen its own way but would just like to see it through completely.

Thanks