There is not really a right answer to this, because you are defining the composite scale. It is what you say it is. The question is what kind of composite scale is relevant to answering the question you are interested in answering.
I suspect that given the very small number of "don't know" responses, you will lose very little information by just coding the "don't know" responses as 3s, which is by far the simplest solution. Then you can move on to worrying about problems that affect more than 2% of your data, which there surely are given that you are looking at survey responses.
The one caveat to this suggestion is if you really can identify some important (for your application) difference between "don't know" and "neither agree nor disagree". Ask yourself the following questions. 1) If you took away the "don't know" option, do you think there is any chance that the respondents who gave that response would have given an answer other than "neither agree nor disagree"? 2) Do you think anyone else's response have changed without the "don't know" option? I am guessing the answer to these questions is going to be no.