A couple of weeks ago I saw a video taped from Danish Television (long time ago) with a story of some 6 or 8 danes who build a biiig canoe with space for everyone. It was build in two parts and assembled on site, when they paddled the length of Torneälven.
Getting fishing permits will be easy compared to possible hunting permits (hunting permits are usually easy to get, but there are special rules in Finnmark for foreigners, limiting their access to hunting permits) and possible export / import permits for firearms if you are going to do some hunting (Finland being the only country allowing bowhunting, and taking guns across the borders outside official border posts might not be a good idea...).
Small game season starts in september (a few species in late august). Seasons etc should be listed on this site
http://www.naturforvaltning.no/ - there are English translations too.
You can download a brochure on the general hunting regulations in pdf format here:
http://english.dirnat.no/archive/attachments/01/38/Jakti065.pdf
The brochure is in both Norwegian, English and German.
Renting a canoe may also be a problem as the route will take you across the border to another country... (not all outlets will allow that).
You sure have lots of planning to do, and if there is anything that I can help with then let me know, and I'll try to do my best.
I can recommend the Ally canoes a lot :biggthump I have used my 16,5' DR in both Norway, Denmark, Swaziland and South Africa. Pretty stiff prices, but worth the money (and you will never have storage problems
): ). Best expedition canoe there is :biggthump