No.. if you do a setup assistant from recovery it will load the entire backup.
It is fairly easy to then create a new user.. set it as admin.. and delete your original admin user.. and all the files associated with it. You can also easily just delete any apps you don't want people to use.
Of course it has to all fit on the hard disk.. and if the disk is too small that will be hard.
Remember too, this must the same or very similar computer.. and it causes issues if you still have the same computer on the network.. I think you should just clean install from downloaded OS.. as long as you downloaded the earlier OS in past you can still download the OS again if you didn't keep a copy of it. What OS are you after? Did you previously download it?