Hi again Panic. I'm glad your DS has 'come clean'.
Like Electric, I understand that you want your DS to understand what a wrong, serious thing he has done. But like everyone else, I think it would be a really bad idea to get him to make a public apology. It would be 'social suicide', as people say.
The reasons for this are complex. Firstly, very many children lie to their friends from time to time, and many go through a stage that lasts several months or years. I can think of countless children who falsely say they have relatives who are inventors of great things, fathers who are astronauts and famous explorers, relatives who are on the telly, have been to exotic countries, etc. My own DS1 told people he had a sibling that had died, when two classmates,sadly, had that happen to them within the same term. A friend of DS2's, who actually lives in a little bungalow with his mum and severely disabled sibling, tells people his family is rich and has a mansion.
Some of these are out-and-out lies. Some are embellishments. Some are wishful thinking. Some are attempts at attention seeking. Some are misunderstandings...
Anyway, the point is, kids are very used to it. They learn to take certain 'facts', and certain people, with a pinch of salt... They seem to understand better than adults that Truth can be a slippery thing, especially when you're a child who is trying to make sense of the world and doesn't have full access to the facts, or an understanding of what their words can sometimes do.
If you let this fizzle out, then almost certainly, your DS's classmates will have forgotten about it within a term - it will simply fade and vanish amid all the other lies and stories.
On the other hand, if you make him read out a statement, then you will draw huge attention to his lies. Many of his classmate's won't even have heard the rumours in the first place, but they'll all hear the 'retraction'. Many will go home and tell their parents, and some of them will get their facts wrong, and tell their parents that your DS apologised to his class because his dad hit him. You will cement his reputation as a liar in every classmate's head - and quite likely spread the rumours that you would want to stop. :(
IMO, it is a good idea to get your DS to think carefully about what he has done, but if you want him to write a letter, make it a letter to you, your DH and his brother, not to his classmates. After all, you are the ones who really most deserve an apology.