251 is less than 10 inches across at its narrowest point which seems quite narrow to me but then again I've been riding 265s for the last decade. 255 really isn't that much bigger...
At the end of the day we're talking in millimeters, there are 25.4 of them per inch. So the waist difference between your K2 Believer and my NS Legacy, 15mm, is only about 0.6" -- literally the width of my pinky finger.
At size 11, you're right on the cusp of "wide" and if your boots have been made in the last 5 years they probably have a footprint-reduction technology to reduce drag anyways. A pinky finger one way or the other isn't likely to wreck you.
A few things to consider: remember your feet are not at the narrowest point, so you probably get a few mm's more play depending on your stance. Also, the optimal amount of overhang (both heelside & toeside) is not Zero - you need some overhang to be able to apply pressure to your edges effectively.
251 probably be OK.