Is it safe to get rid of previously saved registration logs. These are the files that appear when I am asked if I want to back-up the files I have deleted, for example, cc 23465488 5432?
I would like to remove all of these except the very latest.

Yes they are safe to delete. They are just the backups of cleaned reg entries, if your system is fine then just keep the most recent. (I trust CCleaner enough that I don't even make backups of what it removes, not that I'd recommend doing the same)