Understanding Logging Priority & Options in Oracle DB
The database generates redo even without archivelog mode, I guess you meant enabling archivelog mode by logging.
What you asked for is not possible.
Conventional path DML will generate redo, it can not be turned on/off per tablespace.
Direct path loads (INSERT /*+ APPEND */, INSERT /*+ APPEND_VALUES */, CTAS, Data Pump import) and maintenance operations (like table move, index build) can bypass logging, but that is not your everyday workload.
You can exclude tablespaces from the backup, but you can not exclude them from redo.