If you just google "Sugar free cookie recipe", you should be able to find some helpful alternatives.
This. If you just cut out 1 cup of an ingredient, that's a lot of stuff. Then the dry/wet ingredient balance is upset, and the cookies wouldn't bake properly.
Honestly, stay away from pretty much any artificial sweetener. Aspartame, sucralose etc, they react within the body differently than normal sugar, and some actually affect your metabolism. The interesting thing about these in beverages is how your body reacts. If you drink, say, a diet soda made with Splenda and has 0 calories, your body still expects it to have the 100+ calories in a normal soda. So when your body is digesting and realizes that those calories aren't there, it starts to freak out at this perceived deficit.
Perhaps look at gluten free recipes, too? So that the wheat isn't affecting your diabetes, either. And you can do research on diabetic-friendly cookies online, so you don't have to much around in the store reading labels.
And do you have any diabetic friends? Maybe join a diabetic-support forum. They'll have tons of recipes and tips!