Would it be alright to substitute some flour with a whole grain flower? (maybe about half?)

Short answer is yes you can replace, ratio is up to you, but half is likely the maximum that would work with most pastry & cookie recipes.
Recommendation: start with a replacement ratio of 1/4 or 1/3 whole wheat, see how the taste and texture change, then raise or lower the ratio next time you bake.
On whole wheat flour, this article is a good overview, including using it to replace white or all-purpose flour.
https://food52.com/blog/11412-a-whole-wheat-flour-primer