Here is the information you need from the DMV who handles boat registrations in the state: http://doa.alaska.gov/dmv/reg/boat.htm
According to that site, this is what is required to be registered:
"All powered boats (including non-powered boats with auxiliary power units) used on any water of the state. (This includes all rivers, streams, and lakes, regardless of size, and all salt water within 3 miles of land.)
All sport fishing guides are required to register both powered and non-powered boats. (AS 16.05.395)
(Effective February 10th, 2005)"
Essentially, if you put a motor on your canoe and plan to use it in the water, it must be registered.
Hope that helps.