The fastest way to get from AK to DTD is probably by taxi.
IF YOU'RE AN ON-SITE WDW GUEST, then if you're talking Disney Transport, the fastest way I can think of would be a bus to Saratoga Springs Resort (SSR) and then walk from there across to DTD. However, this may be frowned upon, and if so I'm sure others will put words to those frowns pretty soon after reading this.
If a bus to SSR isn't "proper" then your next best bet is to take a bus to another resort in the vicinity of DTD, and then get on a DTD bus at that resort. Your best bets for that would be the Port Orleans resorts or Old Key West.
I know I've read of SSR guests and DVC owners feeling annoyed at non-SSR guests taking SSR buses to and from DTD, but the more I think of it, how would this be any different than someone taking a bus to POFQ or OKW and then switching to a DTD bus from there -- seems to be pretty much the same thing to me.
