Whereabouts in the UK are you ? Do you need to go Dover/Calais and do the long slog through France/Belgium/Holland/Germany/Denmark before hitting Norway ? That will 'waste' about 3 days each way.
Or can you look at one of the other ferry routes that take you closer to Norway ? DFDS Seaways run freight services (with limited passenger capacity) from Immingham to Brevik - 24 hours at sea but it will deliver you straight into Norway.
DFDS Seaways' Brevik - Immingham freight ferry shipping route - DFDSSeaways.com/Freight
I did Jersey to North Cape and back in 4 weeks this summer - but spent 9 days stuck with a dead bike waiting on parts ............so 'riding time' was just over 2.5 weeks. Knock off time for getting to North Cape and I reckon it would be possible to get to the Arctic Circle and back in two weeks but you won't have a lot of time to enjoy the scenery.
Take care though, they don't like people speeding in Norway ...........
Wild camping is fine - there are some rules about keeping a certain distance from property but I had no trouble finding places to camp. However campsites are plentiful, well equipped and cheap (typically around £10 to £12 per night).
The campsites also have 'huts' - imagine large, well insulated garden sheds with electricity, sometimes cooking facilities and bunk beds - these were about £30 to £40 per night - expensive if it's just you, but more affordable if you are travelling with others and splitting the cost. Downside is that you will need to stop riding by late afternoon or early evening as I found the huts were all taken if you left it later.
'Must do' places are Trollstigen, and the Atlantic Ocean Road. Geiranger Fjord and Hardanger Fjord are worth a look. Laerdal tunnel is the longest tunnel in Europe but the 'old' road running over the mountain above the tunnel has amazing scenery.
If you want to take a look, a ride report from my trip is here
To the Arctic Circle and Beyond !
Have a great trip, Scandinavia is a great place to ride !