Cousins Subs publishes almost nothing usable - seven mentions of ingredients, all boilerplate, and no oil words. Soybean oil is named on three items and the fryer runs Wesson shortening on five, with the fat undisclosed. Their own PDF hints oil is a standard build portion, which is unreconciled.
Cousins Subs is the least transparent of the sandwich chains I looked at. Their single nutrition PDF mentions ingredients seven times and every one is boilerplate, and there are no oil words in it at all. What I could pin down: soybean oil is named on exactly three items, and the fryer runs Wesson shortening across five items, though the shortening's actual fat is never disclosed. Kraft mayo appears on 17 items but I could not find a published statement for it, so I am not going to say what is in it. That is genuinely where the evidence stops - I found nothing I could fairly attribute to them on additives. One loose end worth knowing: their own PDF treats a half ounce of oil as a standard build portion while their menu feed only attributes oil to three dishes, and I could not reconcile those two, so the real seed oil exposure may be considerably higher than three items.