Why and how the banana is being used in your recipe is important. Sometimes, bananas in baked goods are used as "mix-ins"---not to change the qualities of the batter, but to add interest, in chunks or slices. Other times they're used as a substitute for eggs, mashed or pureed and meant to replace the binding, leavening and moisture of the egg. Based on your dietary motivations and the absence of eggs in the recipe, I'll assume the banana's mashed (wholly or partly) and used as an egg replacer (though applesauce is also used as an egg replacer, and this is hardly your typical drop cookie recipe).
You won't get the same result substituting avocado for the banana in any proportion. You might still get a result that you find acceptable and enjoy, but avocado is about 15% fat by weight, where bananas contain almost no fat at all. Avocado also has less sugar. You can substitute volume-for-volume or weight-for-weight, since either is about as dense as the other. If you make this substitution, I would expect a firmer cookie. At first I thought avocado would have less moisture as well, but the data indicates they have about the same moisture; it's hard to say how the cooking time might be affected without experimenting.
I would probably try a lower oven temperature for the first batch. The problem you may run into is that the oats need a certain amount of time to cook; if your cookie is firmer (because of reduced sugar), the batter may be more likely to become dry or burn on the outside before it's done on the inside. Reducing the oven temperature would help even this out a bit, if it would otherwise be a problem. Less sugar also means it'll be hard to get a chewy-crispy texture.
Messing with the applesauce at the same time... I don't know. You can make your own applesauce out of the least sweet apples you can find (not necessarily Granny Smith) but I don't think you'd see much of a benefit. The applesauce is your only real source of sweetener and moisture in this recipe and both are pretty important to a cookie dough. You'll have to experiment on your own there, maybe with an artificial sweetener and some vegetable puree that has less natural sugar.