She wore a black wig.
Right, and she wore pants. As did Sally Kellerman and Andrea Dromm in the second pilot. Grace Whitney requested that be changed to a miniskirt.
Apparently, this was the first time a second pilot was made for a TV show. The execs didn't want Barrett in the series so Roddenberry made her into a blonde as Nurse Chapel to sneak her into the show. Grace Whitney was sold to the network execs as the female lead. Roddenberry demoted from second in command to yeoman, and then wrote her out of the show.