Entries (that is, an athlete in an event) can be set as Exhibition. Events and Swimmers cannot.
To enable Exhibition Entries, go to Manage Team > Schedule > click the name of the Meet you want to enable this for > Entries > Settings. Set the checkbox for “Enable exhibition individual entries”.
If you mark the entries as exhibition, they will show up as exhibition in Meet Manager too. (Clarifying that it is entries not swimmers that are marked as exhibition).
In Meet Manager there is a setting that will allow you to seed Exhibition entries after other entries.
In Meet Manager, navigate to:
Set-up > Seeding Preferences > Basic > Parameters > Seed Exhibition athletes last
Also, you should be aware that the setting of exhibition has no bearing on whether or not the time is considered "official". An exhibition entry merely means it doesn't score in that meet. The result produced by that swim is still considered valid and "official" if the meet was also considered official.