Last year, I decided to try a no neck turn, and converted my .269 necks to .274. That was perfect for a 220 Russian neck up.
I got a chuckinge reamer, trued a barrel up, and gently run the reamer in, turning the chuck by hand. I did make a guide bushing that fit the large end of the chamber and the reamer to help guide it in the original chamber.
The reamer was held with a small T handle. The reamer will follow the original neck, and the guide bushing keeps it straight. You will be taking a little more out, as you are going from .262.
As Jerry said, be careful to stop exactly where the original neck ended.
By the way, it shot very well. But I panicked and went back to the .269 and started turning necks again.
http://benchrest.com/attachment.php?attachmentid=19179&stc=1&d=1488976020
Just for info, a .269 works great with the no neck turn Norma 6PPC brass.