According to PTG book of chamber prints.
The 338-300 WSM
at the rear of the cartridge is .5586" and .200" forward of that is .5563"
The 338 Ultra Mag at the rear is .5532" and .200" forward of that it's .551"
The WSM is a .0054" larger diameter than the 338 Ultra Mag. You'd need to have it set back enough to clean this diameter up. My advice would be to cut the threads off and start from there, you'll only loose about 1" of barrel.