I don’t recommend substituting the sugars as you need both to get the best outcome - buttery and soft cookies with a chewy exterior. But in theory, you could definitely make these cookies only with white or brown sugar.
Don't roll cookie dough for too long otherwise, the dough will be warm and can cause the cookies to spread flat while baking.
The dough itself is sticky once rolled so I like to roll the balls after chilling it in the fridge. However, if you can work with this dough before, feel free to roll the balls and freeze them on a baking sheet or similar until they harden slightly. 30 min-1 hour should be fine in the freezer.