I have 2 6970's and with one activated I can play Skyrim on high without a problem. I would Suggest gettting a 6950 with the ability to flash the bios to a 6970. There pretty cheap! http://www.newegg.com/Product/Product.aspx?Item=N82E16814161372
If you look on Ebay im sure you could find one cheaper. But with this card im positive you would be able to play the game on high without a problem.
If you have any other question please dont hesitate to pm me!