If you can get the 480 and you know it works, I'd go for it. You'll get the best performance from it compared to the others:http://www.guru3d.com/article/radeon-6950-6970-review/22
Just know it runs hotter and louder than the others. You PSU will be fine with that card.
On the other hand, you could flash the 6950 to a 6970 and it may work. If it doesn't work, you're left with something less than the 480 (but still respectable and better performance than the 560). And if you try the flash, you void any warranty.
I wouldn't bother flashing it for just a one or two fps gain over the 480. Get the 480.