Jesus is speaking about a combination. Often when He makes statements like this, the first thing to do is not to work out from serpents and doves, but rather to think of them in terms of Jesus. In other words, how was Jesus wise on the one hand and how did He have gentleness in Him on the other hand?
Luke says in Luke 2:52 that from His early days, because of His reflection on Scripture, Jesus grew in wisdom. I sometimes say, especially for those of us who don’t have a lot of wisdom, that the Bible has a book that gives you wisdom before you’ve had time to get it; namely, the book of Proverbs. Proverbs tells you how to take the principles of God’s Word and apply them in a world like ours, and the great example of applying wisdom is our Lord Jesus.
At the same time, we see what Jesus says about Himself: “Come to Me you who labor and are heavy laden, for I am meek and gentle in spirit.” That explains what it means for us to have dove-like gentleness.
We could say, “Let’s think about serpents and let’s think about doves,” but the simplest way to understand what Jesus is saying is to look at how He illustrated and exhibited the qualities of wisdom and gentleness.