Can you use cookie cutters on sticky dough?

That looks like a delicious recipe, but not one that will hold a cookie cutter shape. When a recipe says to space the balls of cookie dough four inches apart, you can expect them to spread in the oven. Cookies that spread will not hold a definable shape. There's no hope of getting this recipe to make cookies that hold a shape.

There are oatmeal cookie recipes designed to be rolled out and cut into shapes. For example, Chewy Oatmeal Decorating Cookies and Oatmeal Rollout Cookies. You might be able to add miniature chocolate chips, but they may make the cookies crack and fall apart. Finely chopped or grated chocolate would probably work fine.

If you feel like experimenting (and are willing to risk having some "failed"* batches of cookies), you can experiment with increasing the oats in your recipe. I haven't made this exact recipe, but I've made many batches of oatmeal cookies with varying levels of oats. I've found that you can use up to double the oatmeal called for in a typical oatmeal cookie recipe before the dough becomes too dry to hold together. Additional oatmeal gives a stiffer, dryer dough that will come closer to holding a shape. The finished cookies will be a bit dryer and a bit less sweet. The large oat flakes in your recipe (since it uses old fashioned oats) will still give the shapes slightly irregular outlines, so don't expect to get a lot of detail. But simple shapes like a heart, star or diamond should still be identifiable in the finished cookie.

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*Where "failed" means not perfect, but your kids/coworkers/classmates will still eat them. If you are the only one eating your cookies, baking experiments can be hazardous to your waistline.