I bought an AWD dakota that has 245 tires on them and I was looking to buy a spare, I found one but its 265, the rest is the same. Would this be a big enough difference to where I couldn't use it without risking drivetrain damage from the imbalance of the different sizes?

 

On an AWD, all four tires MUST be the same size, else things break. Check around the used tire dealers in the area, quite likely someone will have something that will work.

I haven't carried a spare tire on my truck for more than 10 years......