Case head size differences - .473 for the 06 or the 7 and 8mm Mausers, .531 for the Wthby Mag, so you may need bolt face work. Overall length on the 06 is a bit longer than the 257, running about 3.34" to the 257s 3.26" so the feedramp should not be a problem.
This project may require some real gunsmithing advice. Why don't you run this down on the Gunsmithing Forum and see what they say.