The two new 255's will help, but you have two problems still with the tires. The wheels are surely the reason for the tires to be too close, hopefully you can use spacers to improve that. But also the two different sizes will be bad for the transfer case and the front driveshaft. The difference in diameter for those two sizes, when new, would be about 1/2", but with the 265's worn some, that will be closer.
Depending on the actual size difference, you may not be able to put a new driveshaft in it, until you four matching tires. The 4WD system is nothing like the AWD of the V8's, so it has differences that may allow you to disable it, and it works differently when it is activated. The AWD type is full time, and would build heat constantly and lead to failure of the AWD eventually. Your truck with 4WD instead, is an automatic system, it reacts to the change in speed of the front versus rear. That also would hurt the TC eventually, but because it has electrical controls and clutch engagement, it's possible to alter the wiring and control when it can function.
If you drive it with the two different tire sizes, it would be wise to leave the front driveshaft out, or wire in a switch to disable the 4WD. That's an old common trick you can read about here by many people from 1015 years ago. It's called the "brown wire mod" and it simply places a switch in the wire that sends current to the TC's internal clutch. It's a brown wire, and easily you can access it and run two wires from a convenient place that you cut that brown wire, up into a spot inside to a simple switch. I've never done it, but it's easy and it would let you save the transfer case from damage. Get proper size tires on it when you can, maybe consider different wheels depending on those you have(the offset and width, hub center size etc).
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