First point, it was the apostle Matthew who reported Jesus' compassion for the weary multitudes who appeared (spiritually) as sheep having no shepherd. Then Matthew reports Jesus' actual words that all his disciples need to heed when they view spiritually weary multitudes - "Pray ye therefore the Lord of the harvest, that he will send forth labourers into his harvest" (JKV).
If you wanted a biblical example of Jesus mixing his metaphors, you should have quoted what he said in John's gospel account: "I am the light of the world... I am the way, the truth and the life" (John chapter 8); "I am the door of the sheep... I am the good shepherd... My sheep hear my voice" (John chapter 10); "I am the true vine and my Father is the husbandman" (John chapter 15).
So, the answer to your question is that the example you give in Matthew 9:36-39 is not really Jesus mixing his metaphors because he only states one metaphor. Matthew wrote the other one.
But given how much Jesus mixed his metaphors as in those examples in John's account above, the answer is "Yes, Jesus frequently mixed his metaphors." It's not a sin to mix your metaphors (in case you're wondering).
As for the suggestion you offer in your closing sentence, Jesus himself says he is the good shepherd, his sheep knowing his voice and following him. They will not follow hired under-shepherds (John 10:1-5). The metaphors Jesus employs are appropriate for the context in which he states each of them. He was speaking to people working in agriculture, working with flocks, and fishing. He used different metaphors for specific purposes, and when he mixed his metaphors, those who knew and believed his teaching would appreciate the application of them all.