I was under the impression that the "secret characters" unlockable through time, and some characters only exist in the PSX version of the game.
These are the characters (secret and otherwise), according to a FAQ I found, available in the HNG 64 version of the game:
ANDY BOGARD
BILLY KANE
GEESE HOWARD
JOE HIGASHI
KIM KAPHWAN
MAI SHIRANUI
RAIDEN/BIG BEAR
RYUJI YAMAZAKI
TERRY BOGARD
TOJI SAKATA
TSUGUMI SENDO
XIANGFEI LI
Duck King appears to only be avaiable in the PSX version, according to another FAQ I found. To open him on the PSX:
"Beat the game with every character without losing any rounds or using any continues"
Hope this helps.