Can you get a second opinion, or speak to the actual anaesthetist?

I haven't had an operation while pg (but have a friend who did, under GA) and I had an operation while still exclusively breastfeeding pumping. They did the anaesthetic by epidural and a non-narcotic anaesthetic (I think they called it a "twilight"). I was still completely under, but it wasn't as invasive as a normal GA. But they gave me three options - I could have what I had (which was the anaesthetist's recommendation) or a GA or just the epidural and be awake during the op.

So maybe there is another option for you which hasn't been discussed? Like the twilight with a local, or something?

Get another opinion, and find out all your options.

I hope it goes well and you get some good advice.