Here are a couple of things to think about concerning Jesus' quote in Matthew 10:16
First off, Jesus was instructing the disciples in verses 5-15 concerning their short-term mission in Galilee. They were to go to the Jews, preach the kingdom of God is here, travel lightly and bless those who help them along the way. All the verbs are in present tense in this section.
Now Jesus is instructing them about their (and our) future ministry. All the verbs through the end of the chapter are in the future tense. He is preparing them (and us) for the adversity they will face. That is the "sheep and wolves" bit. What are serpents depicted as in the Bible and Jewish culture? A picture of Satan, to be sure, but also depicting shrewdness, cunning and deviousness. The dove is seen as innocent and pure. For the disciples to last against the established religion and to face the adversity, they needed to be smart and non-aggressive. They needed the cunning of the serpent without the venom. A serpent without the traits of a dove is just devious. A dove without the traits of a serpent is naive and gullible.
We need to use the brain, the gray matter God gave us. We are only to preach the Gospel and share our lives with people. We are not to beat them over the head with a ten pound Scofield Bible. We are to love them, not argue with them. If we are rejected, it is Christ they are rejecting. Shake off your sandals and keep going.