We would have to be a guide in order for that to work, if legal to swap hunts in AK and WY... Some states are pretty picky about that stuff, but if done right (as friends) it could be possible... Just not in AK for sheep, unless the person in AK was a guide.
That gets asked every few years, and Nick is correct. You can trade a hunt with a guide, but not an Alaskan resident. If you have your own outfitting business you would have a better ability to swap a hunt with a AK resident guide. But you have to ask yourself is your elk hunt worth $15,000? Most guides up here will not think so.
I have read accounts of non resident guides taking part of their compenstation in a guided hunt from their boss, or where they brought a couple of customers in and were allowed to take a sheep as part of that deal.