No. It is not possible "that reducing cholestrol would lead to a direct, causational decrease in cortisol production?"
There is a little and a bigger flaw in this thought. Cholesterol is not "bad" and it is not an essential nutrient. That means, reduced intake of this substance results usually just in increased synthesis of that substance.
Cholesterol (from the Ancient Greek chole- (bile) and stereos (solid), followed by the chemical suffix -ol for an alcohol) is an organic molecule. It is a sterol (or modified steroid), a type of lipid molecule, and is biosynthesized by all animal cells, because it is an essential structural component of all animal cell membranes and is essential to maintain both membrane structural integrity and fluidity. Cholesterol allows animal cells to function without a cell wall (which in other species protects membrane integrity and cell viability); this allows animal cells to change shape rapidly. (Wikipedia)
Further, it is not true that high cholesterol > leads to/causes > high cortisol > leads to/causes > high stress. It is more the other way around. Reduce stress and you reduce cortisol production and bad levels/ratios of lipoproteins ("high cholesterol").
The second major physiological stress, the HPA axis regulates the release of cortisol, which influences many bodily functions such as metabolic, psychological and immunological functions. (Wikipedia to compare with.)
Completely blocking cholesterol intake and synthesis would be quite deadly.