How can I make these cookies less sweet without ruining the texture?
As I'm sure you know, sugar has many functions in baked goods, so replacing it can be tricky. Syrups will make your cookies too moist and just reducing the sugar can change the texture and browning. Sugar alcohols can add sweetness, but they usually don't brown and they can give people "digestive issues". I think your best route will be replace at least some of the sugar in your recipe with a different type of sugar, while keeping the total amount of sugar the same. 

I think your best resource may be a brewing supply store, as they often sell other types of sugar to help control fermentation in beer. Brewing sugar, also called corn sugar, will be easiest to find and it's almost entirely glucose. In your case, granulated glucose will have the advantage of only being about 70-80% as sweet as sucrose. If this reduces the sweetness too much, you can try blending the granulated glucose with regular sugar. There are other sugars that are even less sweet, like maltose or lactose, that could be used to replace some of the regular sugar in the recipe, but they can be harder to find.

For reference, here is a chart of the relative sweetness of various sugars and sweeteners.