It does automatically (after you click what you have to click), I do not use that software so I might not be the right person to help you, but as far i know it does a great job converting even huge databases.
.:: I met php the 03 December 2003 :: Unforgettable day! ::.
Server specs (Server OS / Apache / MySQL / PHP / DragonflyCMS):
CloudLinux / Apache 2.4 LSAPI / MySQLi 5.7 / PHP 7.3 / head
I don't know how to do it with UltraEdit either. I must have done it the hard way, which is as you described above. Find a messed up character, see what it is in the data, replace with the UTF8 appropriate character. Rinse, lather, repeat. I also did it all in phpMyAdmin because my posts text table is big.