Yes, there are shuttles to Lyttleton and to Christchurch. The first is free, the second has a cost (around $15). This is assuming NCL does what other lines have.
There are now several threads with this as a topic.
You are likely to dock in Lyttleton, it is a working port so you cannot just walk out. There will be a free shuttle to the town, there is also a shuttle to Christchurch for around $15.
The recommended times by most cruise lines are for international flights after 2pm, however, after noon would be easy enough. Personally, I would spend the night and fly out the next morning/day on a flight time that suits my schedule better.
I am hobbling along fairly normally now, with no aides but smaller steps (no strides or speed), at least until March when I have the reconstruction surgery. Then I will be in a cast and then boot for a minimum 10 weeks, with crutches or such. After that who knows.
Happy new year to you and Pat as well.
I am not sure if Royal will have the same as HAL, but there was a free shuttle service into Lyttleton, and a paid shuttle service into Christchurch ($15).