How can I make these cookies less sweet without ruining the texture?

I've finally found a snickerdoodle recipe that results in cookies with that perfect "bite": a crispy outside -- not crunchy, but an almost-infinitesimal stiffness that resists your teeth just a little before "letting them in" -- leading to a chewy-soft inside that is neither too chewy nor too soft, but perfectly in between. The cookies also have a perfect balance of cinnamon vs. vanilla: they're snickerdoodles, not cinnamon cookies. (Well, unless you accidentally use the 1/2 tablespoon measure instead of the 1/2 teaspoon. Don't ask me how I know this.) The problem is, the cookies are just too sweet for my taste. They're not so overly sweet that I can't eat them, but every time I do eat one, I find myself wishing it weren't so sweet.

How can I modify this recipe to make the cookies less sweet, without ruining their texture?

Ingredients:

1/2 cup butter, at room temperature

1 cup sugar

1 egg

1 teaspoon vanilla extract

1 3/4 cups all-purpose flour

1/4 teaspoon salt

1/2 teaspoon baking powder

1 1/2 teaspoons cinnamon

2 tablespoons milk

1/4 cup sugar + 1 tablespoon cinnamon for dipping

The method is the usual: cream butter and sugar, add egg and vanilla, then the dry ingredients, then the milk. Chill 30 minutes, then form into big balls - 1 1/2 inches, dip in the cinnamon sugar, put on parchment- or silpat-lined baking sheet and flatten slightly. Bake at 375°F for 10-12 minutes.

(I followed the recipe almost exactly¹, except for substituting 3/4 cups of the AP flour with WWW [white whole wheat] flour.)

¹_{OK, so I followed the recipe almost exactly the second time I made it. The first time, well, let's not talk about that. Stupid capital T vs. lowercase t.}