You have to do what you are happy with - this is just my experience and is in no way meant in a judgy or you must do way, so please don't take it that way.
I had my pfb dd just over 6 months ago. Just as I fell pregnant, my DP got arrested for something that happened 5 years before I even met him. His solicitor told him when it went to court he should be fine and not to worry.
Roll on to 8 months pregnant, sat in a court 4 hours away from home, and watching DP be told he was sentenced to 6 months, he would have to serve 3 months, if he was careful he might be able to serve some of that time on home tagging.
A month later, I haven't seen DP as he was in a London prison and I couldn't travel the 4 hours. I'm taken in to hospital as baby's heartbeat can't be found, there's to and froing over induction and c section, I can't speak to DP about any of this, only the Chaplin of the prison who I don't know from Adam, and when DP could call he had to be mindful how long he spent on the phone as phoning mobiles cost so much.
I was lucky my mum and dad made it in time to be with me, because to be perfectly honest, I needed someone there who knew me, and could help calm me in the scary moments and keep me going when I was ready to give up.
I know I had no choice about DP, and it's something I still find hard to this day, he missed an important part of our life together. For having been an idiot before I even knew him. We couldn't have any say in what happened, but I hated not having him there.
Do whatever you are happy with, that is vital, and something only you can decide on. But consider everything and if you need to tell him he never mentions it again or can only stay in once corner of the room. Just remember it can be an awfully long time to be 'alone' for.
What ever you decide I hope it all goes well for you, the best part is being handed your bundle and knowing all the hard work has paid off.