Find out what the mfg says about 1 different sized tire on a 4x4. It is a 4x4 correct?
First and foremost there are many Alaska trip areas where there is no tire related shop for many miles, think hundreds. This can/does also include most of Canada. Plus when you get they may not have your size and getting one could take days.
My advice is be prepared. Take one full sized mounted tire and consider a unmounted spare for extra caution. And note that even the same sized tire may not have the same diameter due to wear or other differences due to brands so that could be a consideration for longer distances.
Our round trip mileage was 9600 miles.