Pickles, either fermented or made with vinegar, are considered preserved because of the acid, not any sugar that might be added. Unlike jams, which need the sugar to keep them from spoiling. Personally, I would either leave out the sugar called for in a recipe, or severely cut back on the amount. And nowadays would use erythritol or stevia if I used anything. Or, more likely, I would look for a different recipe :-)

Answering another post of yours: the Germans often add a chopped apple to their red cabbage, not sugar. If apples are on your OK list you might try that.

ETA: The red cabbage post was from Meme; sorry about that.