You aren't going to care - all you're going to care about is having labor be over! You don't care who is in there, who is watching - my only concern was that my husband had better be pushing on my back harder because that was the only thing that made the pain bearable. I had back labor 4 times and no drugs. I thought I didn't want any other men in there because I had used midwives and had home birth 2 times, but with baby #3, I was in the hospital, I had 2 drs (one was a male resident dr) and He ended up holding one of my legs and was there for the whole show and I could have cared less! He cried tears of joy with us when our daughter was born and told us how beautiful she was, etc... (he and his wife were trying) I am a fairly modest person, but in labor - all you think about is not being in pain and delivering your baby safely. I seriously only had a good experience each time, having my 4 children.
If you think you're going to be really distracted in labor by extra people, put that in a written birth plan - "I only want my husband, my doctor, one nurse and that's it - as long as everything is progressing and there is no emergency"
When I had my daughter, we only had 2 drs and 1 nurse and one dr was being trained. They had asked me if it was okay for him to be included and I admired him as a person, so I thought it would be fine. I also had been in labor 2 times before and knew when it got down to pushing I wouldn't care who was in there.
You have to realize that the professionals you have surrounding you when you have that baby have seen it all! Bodily functions which you seem to be embarrassed about are EXPECTED to happen during birth - think about it. When a mom is pushing with all of her might to give birth to a child who weighs 6-10 lbs, do you honestly think you can control not pushing anything else out from other places? It cannot be helped and the drs, midwives and nurses all realize this. No one will say anything to embarrass you - they are there to help you and your baby be safe.
It's something all of us have thought about with #1, you don't know what to expect and you read things. Don't worry about it - I can assure you, all of this is going to be the last thing on your mind when you're in labor. Surround yourself with a support system - someone who is there to make sure your wants and needs are being addressed, like a Doula or something. That would be a big help. You're going to need to focus, relax, have peace, etc... so whatever you need to have that - set it up for yourself and you'll be fine
Best Wishes!