On every Japanese version of the Crash games, Japanese Crash appears on every cover, but he rarely appears in the games themselves, as Crash's model is not edited in-game. Some of his in-game appearances are on FMV videos included as extras in the first games, some icons and in the title screen of Crash Team Racing.
There is a code to unlock the Japanese Crash skin on the PS2 version of Crash Tag Team Racing. On the start screen, hold L1 and R1 and press Square, Circle, Square, Circle. If done correctly the player will hear a chime. The skin can be available for either Adventure Mode or Multiplayer mode. But when players enter the code, they will find the normal Crash which they are trying to race in Adventure Mode will have no pupils.
Although you can only use the regular Japanese Crash skin in the NTSC-U and PAL versions, the models for the other costumes are still in the game files, as seen here in the DEFAULT.rcf: