Mine was 10 days too and initially to land and fly off from CC. However 10 days was too short to do the recommended anti-clockwise route so we ended up paying a little more to fly off from Queenstown >> Auckland >> SG which was actually a good choice I feel.
If I had a choice to go there again, I will plan 2 weeks to do the recommended anti-clockwise route then can get to experience the FJ Glaciers.
The problem was the rented car because if you rented the car from CC and drove to Arthur's Pass>>Greymouth>> FJ Glaciers, there is actually an option to take an expensive heli ride to cut across to Mount Cook. Lol...... but I wasn't sure if I could just leave the rented car at FJ Glaciers. (Maybe some expert traveler can comment)
Anyways I went,
CC >>Akaroa >> Lake Tepako>> Mt Cook >> Twizel >> Wanaka >> Queesntown >> Milford Sound >> Queenstown
For 10 days trip, if wanna chiong, you might need to forgo Milford sound I think...