There are no buses from the CR to the BW, and the Beach Club is closer to IG than BW.Your only other choice would be a bus from the contemporary to the Boardwalk and enter EPCOT at the international gateway. Then walk to Norway.
Taxi to the Beach Club, then walk to the International Gateway, in, up the ramp, halfway around World Showcase Lagoon to Akershüs.
If it's before park opening, there will be a rope and a CM preventing you from walking to the right, by way of France, to Norway.If you take a cab, it's going to cut off a lot of the time it would take to use the monorail....have to monorail over to the TTC (and subsequent wait times at the CR), then transfer to the Epcot line, again, with subsequent wait times. Then the ride to Epcot (about 10+ mins), through FutureWorld, about 15+ mins, and over to Norway, about 10 mins. So, you would need about an hour doing it that way.
If you take a cab, from CR to BC, the cab would be about 15 mins, tops. Then walk to the Gateway, about 10 mins, then over to Norway, 8+ mins...about half the time.
When arriving at BC, you would walk through the lobby area, out the rear door, facing the lake. At the sidewalk, go left and keep going up the hilly area, and down to the International Gateway. Once into the park, head to Norway...I usually go right at the bridge, but it's pretty equidistant going either way at this point.
I also checked from the Boardwalk and its about the same or even a little less since I think its a straighter shot.
The "straighter shot" is from the back of the Beach Club to the IG entrance of Epcot.
I rechecked Google Earth and its almost exactly the same distance from where I think a taxi would drop you off at both resorts to the IG.
I'l try to figure out how to post the pic with the paths drawn to see if I missed something.
Also "straighter shot" was not the best term to use.
As far as I know your best bet is to take Monorail to TTC, switch to Epcot monorail, go in main entrance, and then hoof it to Norway. This process really will not take that long! We just got back and did similar scenarios for 10 days!
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This is how I'd go from the Contemporary, IF the monorail were running.
If I were taking a taxi, I'd rather get dropped off at the Beach Club, because I think the walk through an empty World Showcase is prettier than through an empty Future World.
As posted above though you will be ushered around to the left and not the right through the World Showcase at that time.
The left is the shorter way!
**Didn't see your previous post until after I posted this. If one could walk to the right around World Showcase past most of the countries, that would be the most scenic walk - although I love walking past the UK and Canada.