Wowza should really be run as a different user. I suggest creating a dedicated user and group for Wowza. Any files created by Wowza will be owned by it's user and it's primary group. To create the user:
groupadd wowza # Create a group for Wowza
useradd -c 'Wowza Media Server' -d /path/to/media -g wowza wowza
The above command will create a group called wowza and a user called wowza. If needed you can invoke su as a wrapper around it to run it as a different user:
su -l -c 'umask 002; wowza-media-server' wowza
The above command when run from root will invoke the command wowza-media-server as user wowza. The command wowza-media-server will be running as user wowza and any files it creates will be owned by user wowza and group wowza. The
umask 002 ensures that any files created by wowza-media-server will be group writable. Then you can add users to that group and they will be able write to any files created by wowza-media-server.