brine is water + salt basically , so no real fat except that which leaks out of the fish into the water. olive oil and sunflower oil, are oil, fat. if you have to go low fat the brine, but, why aren't you eating fat, fat is very good for you. What about mayo, its basically eggs, its good quality fats.
Can't remember off the top of my head if sunflower oil is crap for you though think its not great, olive oil is a good fat for you aswell, uncooked its very good for you, not as good in cooking as its fairly unstable and heating damages it.
if you're losing fat I can tell you right now that the key to fat loss is NOT trying to drop all fat from your diet.