Whole wheat flour behaves very differently from all purpose flour. Sifting will help, but you will still have lots of bran and protein left.
It's not recommended to use pure whole wheat flour for baking, except where you want the effect (as in pumpernickel, for example). You'll get cookies which will be rather tough, moist and will seem underbaked (but no amount of baking will remove the impression). Nothing crumbly about them.
The result will be edible, but very different from a standard cookie, and it is questionable that you will like it. Still, if you are feeling adventurous, you can try it out and see if it's what you want.
You could try to mix your whole wheat flour with pure starch, which will make the result more cookielike in texture, or also some non-wheat flours such as quinoa flour. It still won't be like a classic cookie in texture, and the taste will be unusual too.