Unfortunately for you, it's not the 'People' that treat AK as a different country. It's the shipping companies.
I would have no issue shipping to AK, except:
For example, consider a 12# box 12x12x12. Reasonable size for a trade, but just making up some numbers. Using FedEx.
For me to ship to... the cost is..
Florida...$15
So-Cal...$22
...
Anchorage...$72!!!
I've done several trades for "local shelf beer,' its fun to do, and alot easier than trading for anything "special." But in this case, the shipping just drives it up way too much!
But, I wish you luck! Trading beers is fun, but not cheap for sure!