Hi Massimo M,
Thanks for providing so detailed information about the environment. What you have mentioned is possible. You can first move your mailboxes to Exchange Online.
You also said you want to create new public folders (PF) in Exchange 2010 server, and manually move the messages from Exchange 2003 PFs to Exchange 2010 PFs. Based on my experience, this is possible. To make the Exchange 2010 SP3 public folders visible to online users, we need firstly move the PFs from Exchange 2010 to Exchange Online, because cloud users do not have access to on-premise PFs, cross-premise is not supported on this situation. And we also need to remove the PF replicas from Exchange 2003.
About how to migrate public folders to Exchange Online in hybrid deployment, please refer to the article in the blog above.
Thanks,
Young Yang