birth photography questions??

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So I am really interested in the idea of hiring a birth photographer but they are very expensive and I am definitely not able to afford something like that with this pregnancy. I don't want to ask a family member or friend cause I feel uncomfortable sharing something so intimate like giving birth to my child with anyone but my partner and obviously the doctors that will be in the room I would also be comfortable with a photographer as it is not really necassirly an intimate moment for them since they are serving the purpose of doing a job and they have no emotional connection to me therefore doctors and people who are not related do not bother me if they are in the room if that makes sense. It's like since family and friends have a relationship with me and I love them but them being apart of certain moments like me giving birth to my child is not something I'm comfortable sharing with them because it's not really a moment to be shared in that way if that makes sense I'm sure some can relate and understand I'm saying I'm just not explaining well. Anyways I was wondering if it would maybe be ok to ask a nurse or someone else in the room at the time to maybe snap a few photos like the first time my partner and I see our baby and hold him in our arms, do you think that's inappropriate to ask something like that or do you think that would be ok? Do you guys have any suggestions on how to capture this moment with it being cheap/free ?