The character set is a database level property and changing it typically does incur some down time.

It is possible to use export and import to do a character set migration, but we typically recommend that you do a full database export and import to properly convert all data to a new character set.

It is theoretically possible do it one partition at a time, but you would have to work out some way to cut over the newly inserted data, which would most likely incur a little down time.

Regarding the locking of the table while exporting the older partition, and inserting into the latest partition. You should not encounter any problems as long as both operations explicitly list the partition they need to operate on.

Also, you would need to make sure that all columns with character data types have been specified as large enough before the import to handle an increase in column value sizes.

We would strongly recommend you consult the Database Globalization Support Guide

http://docs.oracle.com/cd/E11882_01/server.112/e10729/ch11charsetmig.htm#NLSPG011

And consider using the Oracle Database Migration Assistant for Unicode, which is available on OTN
http://www.oracle.com/technetwork/database/database-technologies/globalization/dmu/overview/index.html