What is your reasoning for wanting to cut sugar? It kind of matters, because if you are concerned about blood sugar/insulin resistance, you should know that artificial sugars and sweeteners can spike insulin the same as real sugar does. If it's calorie reduction, and you don't care about the metabolic effects, you can try something like Swerve or Splenda for baking, although I have found that both have an unpleasant aftertaste.
I agree with this. WHY you want to cut sugar is important. You say you don't care about carbs, but sugar IS pure carbs. Then it metabolizes in the body to become fat if not burned away. If you don't want to spike your blood sugar levels, look for recipes with higher
ratios of protein, fat or fiber. Any/all off them will mitigate sugar, making it then digest slower in the body.
High protein recipes are usually designed to be higher in protein, less sugar/carbs.
The shortbread suggestion has a higher ratio of butter/fat and less sugar.
The oatmeal raisin cookie is very high fiber. While the recipe says no sugar added, unless one uses a sugar-free applesauce and sugar free chocolate chips, there is added (hidden) sugar. So again, knowing why you are cutting sugar determines how much sugar a recipe really can have.
Many of the
newer diabetic recipes and Weight Watchers recipes - created in the last year or two, are designed to be higher protein, less carbs, as the organizations realized controlling diabetes and weight isn't simply eating less sugar. So you might want to look at those recipes. Recipes stating they have a low glycemic index will also mean they have a lower sugar ratio.
Also, as simplistic as it may sound, as a PP stated, allow yourself to have your favorite indulgence, but eat LESS of it. WHEN you eat them matters. Make sure you eat protein before or with it. If one eats the protein first and saves the cookies for when they are full, they will be less likely to gorge on many cookies as though they are a meal. Two cookies, consciously and slowly savored may suffice, instead of the 5 cookies usually gobbled down without much thought. How many of us have savored the first two
bites of something, then plowed through 4 more cookies or a half bag of chips and realized afterward, we weren't really paying attention to eating them beyond those first two bites?

I know I have. I eat my sweets (and fats) much more consciously now, and therefore eat less of them.