I don't have all-purpose flour at hand right now, so I'm thinking of making chocolate chip cookies with whole wheat flour.
What difference will this make in terms of texture/taste/cooking time? Also, if I sift the flour using a very fine sieve, will it make the cookies better?
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.
I made chocolate chunk cookies with whole wheat flour, sifted whole wheat flour and all purpose flour.
The picture didn't come out good, the cookies were thicker and lighter in color than what they look like here.
The cookie with whole wheat flour was denser and barely spread out while baking. It also had a very different "whole wheat" taste.
The one with sifted whole wheat flour was somewhere in between.
I won't be making whole wheat flour chocolate chip cookies (if the recipe calls for all purpose flour) again, but I won't mind the ones with sifted whole wheat flour.
As @rumtscho says, whole-meal flour is going to behave differently in many ways -- hydration, handling, mouthfeel... That said, certain preparations of baked goods will tend to hold up better to these properties of whole-grain or coarse-grained flours -- often this amounts to more sugar and fat! Though you're not asking for a recipe, my response is... make a different kind of cookie!
No brand loyalty here, but King Arthur has a breadth of whole-grain recipes including sweets. I like this one for a relatively simple whole wheat oatmeal cookie. The quantity of sugar (>2/3 cup) and fat (full stick of butter!) along with the coarseness of oats help normalize the assertive whole-meal flour.
Here are some of KA's other suggestions.
Good luck!
