Itinerary fine-tuning

Hi all, I know this has been posted ad nauseam but just curious from those who know if my itinerary is realistic/if it puts too much time in one area (or not enough in others).

My concern and main question is do I need two days in Mt Cook and if not should I shift everything back a day and add a day in Wanaka or Queenstown?

I haven't fleshed out what I am doing in each area yet either so I am not going in depth on the plan for each day too much but general idea so far.

Worth noting, I am not an advanced hiker, though I am fit, but only want to go on scenic walks/easy hikes, try some wineries, would love to kayak or swim. It will be early spring/September in NZ when I go though so I know thats not the best time of year for everything (also any guidance on time of year is appreciated).

Here is the itinerary, let me know what you think. Yes, I know tourist heavy. THANK YOU!

Day 1

Arrive in Christchurch, rent car, walk around/grab food, keep it chill

Day 2

Easy morning in Christchurch, possibly linger or not then drive to Lake Tekapo, possibly stopping at Rakaia Gorge along way, check out the church late afternoon, stargaze, go to bed.

Day 3

Travel to Mt Cook and stay in the park. Stop at Lake pukaki along way. Do the Hook Valley Trail.

Day 4

ANOTHER FULL DAY IN MT COOK? OR WHAT OTHER OPTION?

Blue Lake, Lavender Farm, other trails? Maybe too hard the other trails.

Day 5

Mt Cook to Wanaka [unknown scenic activities]

Day 6

Wanaka (hiking/scenic stuff)

Day 7

Wanaka (wineries/breweries/food and relax)

Day 8

Wanaka to Te Anu

Unknown activity yet

Day 9

Te Anu to Milford Sound (and either back to Te Anu or overnight cruise)

Day 10

Either Te Anu to Queenstown or Milford sound if overnight to Queenstown

Day 11

Queenstown

Adventure

Day 12

Queenstown

Foodie/Wino

Day 13

Leave/full travel day