Should my son's apology be public because his hurtful comment was public?

My eight-year-old said another child's lunch "smelled like the bin." Three children laughed. His teacher told me at pickup, and he admitted saying it.

I asked him to write an apology that evening. He wrote, "Sorry you got upset." I made him start again, then suggested reading the letter to the whole class so everyone who heard the comment would hear the apology.

His teacher has offered to help him apologize privately first. My partner agrees and says I am turning the repair into a performance. I keep thinking the other child was embarrassed publicly while my son gets to say sorry quietly.

I haven't asked what the other child wants, and I don't know whether a class announcement would bring more attention to the lunch. My son needs to take responsibility for the remark and the laughter he invited. How do we do that without making the child he hurt sit through another scene arranged around his food?