What flavor is the cookie? Adding the needed butter won't cause you any problems, as long as you work it as little as possible. Make sure the butter is very soft.The issue is that the eggs (and the butter to a small degree) contain water. As the flour is worked in the presence of water, the flour proteins (gluten) begin to become elastic. This will either make the cookies more bread-like, or just plain tough. They won't be that soft, gooey cookie that you're looking for.
If you carefully add the remaining butter, preferably by hand, without overworking the dough, you will have no issues.
The smoked paprika will actually work with some flavors, such as butterscotch, and chocolate chip (if it has brown sugar in the recipe). I've actually added crisp, smoke bacon bits (freshly made) to my butterscotch cookies before, with rave reviews. But, it won't go will all cookie flavors.
Hope that helps.
Seeeeeeya; Chief Longwind of the North
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