There are ample boats out there for much less than you have saved up. And if you can live in a shack then you can live in a small boat.
I lived on a 25 foot hunter for 4 years in Michigan all the way to St. Thomas. The benefit of living on a small boat is you won't have any rent expense compared to an apartment. Infact there is a 36ft Cal for sale in Holland, Michigan for $7k right now and it's in pretty good condition. But I took the 12k a year I would have spent on rent and put it into the boat and my savings.
To make this dream a reality you might consider moving from Alaska. Keeping warm in a small boat in northern climates is tough. Besides trying to cruise the Bearing Sea in a small boat might not always be pleasant or safe. But if this is a dream that won't stop then do it now. Get the best boat you can for your money and go cruising. You can get experience by volunteering as crew at your local boat club. Unless ofcourse if they are ice boats.