Want to change CHARACTER SET of a production database

Our production database has NLS_CHARACTERSET WE8ISO8859P15. Before we upgrade next application version (Automic), the vendor has asked us to change database

NLS_CHARACTERSET from WE8ISO8859P15 to AL32UTF8.

If we execute:

SHUTDOWN IMMEDIATE;
STARTUP RESTRICT;
ALTER SYSTEM SET JOB_QUEUE_PROCESSES = 0
/
ALTER SYSTEM SET AQ_TM_PROCESSES = 0
/
ALTER DATABASE CHARACTER SET INTERNAL_USE AL32UTF8
/
SHUTDOWN IMMEDIATE;
STARTUP;

Will it work? Is it a recommended path?

Thanks,

Unmesh