Effects of reducing sugar in cookies
Sugar isn't added to baked goods just to sweeten them: it also does things to the fats and starches to help create the texture. This is related to why some recipes require castor sugar (i.e. very fine crystals) and others do not. 

One solution you could experiment with is changing the sugar. Dextrose is noticeably less sweet than cane sugar, for instance, for the same quantity.