True smoked fish is not cooked but cold smoked. The brine and smoke is what cures the fish. I had indian cold smoked fish one time. I understand it may take two or more weeks. What I had was the best smoke salmon I ever ate.
Little Chiefs and Big Chiefs are not really designed to "cook" anything. Yes they can cook things but not very efficiently. Having said that, I used my Little and Big chief to cook for years but found that a couple hours in the smoker then the oven or BBQ to finish cooking gave better flavor (objective opinion). The brine, be it sugar based or salts based, is what "cooks" the fish. If you want to cook smoke you would be better off with a Bradly, Brinkman, or some other smoker that you can have better control of the temperature and smoke supply. I have both Brinkman and a Bradly Commercial grade. I use the Brinkman to put smoke on a quick meal (this can also be done in a Weber grill), and the Bradley to do volume, or extended smoking. Controlling the temp, when to smoke and how much smoke really makes a world of difference in taste. Trout smoking has a fine line between just done and to dry. Get a log and record what brine, how long brined, how much smoke, what wood, and temp. That way you can duplicate the good ones and not repeat the not so good ones, lol.