Substituting vegetable oil for canola oil

On first blush, you will probably want a fat or oil with similar qualities as the "vegetable" oil you're replacing, such as olive oil. Butter has a much lower a smoke point, however, cornbread recipes exist that use butter or lard. I'd be willing to experiment, particularly if you're used to cooking with butter. (Just be careful with heat.) As far as quantity, I'd use a bit less than 1/3 of a cup, but that's me being defensive as I don't know the recipe you're using.

Note that basic mayonnaise normally is made from egg yolks, oil, mustard, citron juice, salt and pepper. This is means that the flavors in mayonnaise are a bit sour. This is normally compensated with sugar in the recipe, but you are using a non-sugar recipe.

I think the idea of adding mayonnaise for the texture is ok. However I experienced the effect of making a cake becoming more moist from some other ingredients from which i think they fit more properly in a brownie recipe. You could replace the amount of oil by the same amount of applesauce. Or add some additional applesauce to the recipe (2 tablespoons I would say) The flavors of applesauce do not seem to change the flavor of a cake a lot in practice. And applesauce is used in a lot of recipes to bake low fat. So in stand of sugar free you now have low fat brownies. If you still want it to be sugar free you can use or make some sugar free applesauce of course. If you don't want to use applesauce you good think of adding a couple of tablespoons of vanilla pudding to the recipe. Or even chocolate pudding, to give your brownies even more chocolate flavor. Also replacing some of the water you use in the recipe by some more oil can work. The water while evaporate during the baking. However, the oil does not do that, and stays liquid at room temperature after baking. This causes an moisty effect.

Note that you will almost always add some more sugar/oil in the recipe if you only want to use 'instant' products. If you want to make non-sugar/low fat brownies this may not be what you want. So you could also think about undercooking your brownies a little. So shorten the cooking time a little bit, so you don't cook your brownies 'dry' but still a bit undercooked in the middle. This makes it very moist, and personally I think the 'undercookedness' of brownies it actually the best think about them.