Thanks everyone for your comments. I have looked into all the rifles mentioned that I dint know, and read all links provided. You guys provided a solid base to start with. I have done some other readings, gone to a few gun stores in town, and thought I should post what options I think there is for a light backpack application. Please do not hesitate to comment if I am missing any other similar options.
Using the summary below I might go two different ways. I would like to have a semi-auto mechanism for this rifle. I know this come with extra weight, but partridge for example are often found in groups walking on the ground, so a semi-auto would be more effective and fun in such cases. Semi-auto can also be very useful with hare on the go. For the semi-automatic option I am leaning towards a Marlin Papoose due to the lower weight compared to the Rugger 10/22; and when holding a Papoose and Henry AR7 side by side I preferred the feel of the papoose. It found the Papoose to be a more balance rifle than the AR7, and felt more like a standard rifle.
The other option is to forget about the semi-automatic desire, and prioritise low weight and cost. At 1 Lbs the Pack-Rifle is the best option for a serious backpacker. It also is a takedown rifle, and has a fishing rod and reel add-on. I could even consider taking such a light rifle in a goat or sheep trip! However I added the cost constraint because the Pack-Rifle is currently out of my price range. Another very light setup is a Crickett with a 22LR-PRK kit. Like the Pack-Rifle the final setup weight is about 1 LBS, but its bolt action. However the cost of the rifle and the kit add up on the expensive side for a specialized use rifle.
This leaves me to a Savage Youth Rascal, Cricket, or Marlin with a homemade modification to the stock to bring the weight down, and extend the stock LOP for the two youth rifles.
Marlin Papoose
Weight: 3.25 lb (1.47 kg)
Length: 35.25 in
Barrel length: 16.25 in
Disassembled length: 21 inches (530 mm)
Henry U.S. Survival AR7
Weight: 3.5 lbs
Length: 35”
Barrel length: 16
Disassembled length: 16-1/2”
Chiappa Little Badger
Weight: 2.9
Length: 31
Barrel length: 16.5"
Disassembled length: 17
Rugger 10/22 Take Down
Weight: 4-2/3
Length: 37
Barrel length: 18.5
Pack-Rifle
Weight: 15.5 OZ (0.97 LBS)
Length: 33
Disassembled length: 17
Savage Youth Rascal
Weight: 2 5/8
Length: 31.3
Barrel length: 16 1/8
Crickett
Weight: 2.5
Length: 30.5
Barrel length: 16.15
22LR PRK (Need a Crickett)
Weight: 1 lbs
Mossberg Blaze
Weight: 3.5
Length: 35 3/4
Barrel length: 16.5