I don't think smoked fish is that sweet. A brine with a cup of table sugar in it probably has way more than half of that left in the brine when the fish comes out. Then you rinse, leaving even less behind.

I know this......I can eat quite a serving of smoked fish brined with sugar and see virtually no change in blood sugar. Certainly not enough to warrant substituting out the sugar used in the brine. I'd wager that the crackers people eat with smoked fish will change your blood sugar more than the smoked fish will.

Leave the sugar in the brine.
_________________________
She was standin' alone over by the juke box, like she'd something to sell.
I said "baby, what's the goin' price?" She told me to go to hell.

Bon Scott - Shot Down in Flames