What is the best course of action when dealing with strangers who misunderstand a smile, and how can one overcome the feelings of contempt and fear resulting from this?

We see exaggeration in your words, for not everyone to whom we smile considers it a weakness, and smiling in the face of your Muslim brother is charity. The Prophet, peace and blessings be upon him, smiled frequently. There must be moderation and wisdom in dealing with people, neither excess nor harshness. This applies to believing women and your mahrams. As for disbelieving women, excessive interaction is not legislated except for reasons such as inviting them to Islam. And it is absolutely forbidden to be unreserved with strange men, except out of necessity and according to শরী'আ-compliant regulations.