Matthew 9:12 , Mark 2:17, and Luke 5:31 have parallel passages that all use the phrase
"hoi kakoos ekhontes"
word for word this reads those (who) badly having but it means something like those who are in a continual bad condition. This condition can be one of health or sin and a colloquial translation might be "those who are in a bad way" and its used in contrast to the term iskhontes those who are fit and strong or healthy in Luke who uses hugiaiontes.
This has lead to the word being translated as sick or sinners.
So which to use ?
In the following verse Jesus does use the word sinners however I also suspect this is yet another example of Jesus teasing the scribes and other religious authorities by using a phrase he knew had a double meaning and it is also a comment on the popular belief that sin caused disease.
Sick or Sinner?
The dilemna is how to explain both?
It has however got to be your choice how to explain this.
I hope my notes will be useful for your ministry?