We have a production instance of size 1.3 TB (archive log) and need to increase the db_files soft parameter in the parameter file. Is it mandatory to take the full backup of the database after changing the parameter and recreating the control file? Our backup is very slow, estimated to take 15 days for full backup of the database to complete. I would appreciate it if you could suggest some other safe way without taking the full backup.
You do not have to recreate the control file to change db_files--as you note, it is a soft parameter and you need only change it in your spfile or pfile (depending on which you use).
I wouldn't think a full backup is required after making such a change, but of course that decision is up to you.