I've installed Media Go and created a playlist, then I've added files and sorted the playlist from A to Z based on Artist. Afterwards, I used right click on the left tree menu on the playlist and exported the file to a directory. I've loaded the file on Winamp and it appeared exactly how I sorted the files.
This is the only way to alphabetize it. If the Walkman has auto sorting, then you have to disable this feature from its settings.