You can book 60 days IIRC for the cruise. I believe the rule on alcohol is you can order it, but not bring your own which might limit things. I have not heard that has changed. My birthday trip we had it fully booked with 10 total. Others it's just been my family of 3 and another family we often travel with. Considering asking my 14yo if he wants one though we'll be at Polynesian since other tours were booked (this is a 2 year later redo of a mom and son trip that was canceled days before due to covid closure so I'm being generous with him lol).
The best cruise was when it was just us though and I was hugging my son who had never really seen fireworks close up. I'd totally do it for just 2 and it will feel about as private as you can get. Like I said you are free to talk to the captain too as much or as little as you like.
For my birthday one, it was fun as we anchored for Illuminations (it was my favorite fireworks) there were other boats all wishing me happy birthday before the show started. It is fun to do for sure